dr hab. inż. Tomasz Zieliński 

Doktorat
2004  Metoda impulsowych dystorsji wirtualnych z zastosowaniem do modelowania i identyfikacji defektów w konstrukcjach
 574 
Habilitacja
20160225  Propagacja i tłumienie fal akustycznych w ośrodkach porowatych, a cechy geometryczne i drgania mikrostruktury 
Promotor prac doktorskich
1.  20141127 pomocniczy  Nowak Łukasz  Adaptive feedback control system for reduction of vibroacoustic emission  671 
Ostatnie publikacje
1.  Zieliński T.G., Chevillotte F.^{♦}, Deckers E.^{♦}, Sound absorption of plates with microslits backed with air cavities: Analytical estimations, numerical calculations and experimental validations, APPLIED ACOUSTICS, ISSN: 0003682X, DOI: 10.1016/j.apacoust.2018.11.026, Vol.146, pp.261279, 2019 Streszczenie: This work discusses many practical and some theoretical aspects concerning modelling and design of plates with microslits, involving multiscale calculations based on microstructure. To this end, useful mathematical reductions are demonstrated, and numerical computations are compared with possible analytical estimations. The numerical and analytical approaches are used to calculate the transport parameters for complex microperforated (microslotted) plates, which allow to determine the effective properties of the equivalent fluid, so that at the macroscale level the plate can be treated as a specific layer of acoustic fluid. In that way, the sound absorption of microslotted plates backed with air cavities can be determined by solving a multilayer system of Helmholtz equations. Two such examples are presented in the paper and validated experimentally. The first plate has narrow slits precisely cut out using a traditional technique, while the second plate  with an original microperforated pattern  is 3Dprinted. Słowa kluczowe: Microslotted plates, Microperforated plates, Sound absorption, Microstructurebased modelling, 3Dprinting Afiliacje autorów:
 100p.  
2.  Zieliński T.G., Microstructure representations for sound absorbing fibrous media: 3D and 2D multiscale modelling and experiments, JOURNAL OF SOUND AND VIBRATION, ISSN: 0022460X, DOI: 10.1016/j.jsv.2017.07.047, Vol.409, pp.112130, 2017 Streszczenie: The paper proposes and investigates computationallyefficient microstructure representations for sound absorbing fibrous media. Threedimensional volume elements involving nontrivial periodic arrangements of straight fibres are examined as well as simple twodimensional cells. It has been found that a simple 2D quasirepresentative cell can provide similar predictions as a volume element which is in general much more geometrically accurate for typical fibrous materials. The multiscale modelling allowed to determine the effective speeds and damping of acoustic waves propagating in such media, which brings up a discussion on the correlation between the speed, penetration range and attenuation of sound waves. Original experiments on manufactured copperwire samples are presented and the microstructurebased calculations of acoustic absorption are compared with the corresponding experimental results. In fact, the comparison suggested the microstructure modifications leading to representations with nonuniformly distributed fibres. Słowa kluczowe: Sound absorption, Fibrous materials, Multiscale modelling, Microstructure representations Afiliacje autorów:
 35p.  
3.  Zieliński T.G., Normalized inverse characterization of sound absorbing rigid porous media, JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, ISSN: 00014966, DOI: 10.1121/1.4919806, Vol.137, No.6, pp.32323243, 2015 Streszczenie: This paper presents a methodology for the inverse characterization of sound absorbing rigid porous media, based on standard measurements of the surface acoustic impedance of a porous sample. The model parameters need to be normalized to have a robust identification procedure which fits the modelpredicted impedance curves with the measured ones. Such a normalization provides a substitute set of dimensionless (normalized) parameters unambiguously related to the original model parameters. Moreover, two scaling frequencies are introduced, however, they are not additional parameters and for different, yet reasonable, assumptions of their values, the identification procedure should eventually lead to the same solution. The proposed identification technique uses measured and computed impedance curves for a porous sample not only in the standard configuration, that is, set to the rigid termination piston in an impedance tube, but also with air gaps of known thicknesses between the sample and the piston. Therefore, all necessary analytical formulas for sound propagation in doublelayered media are provided. The methodology is illustrated by one numerical test and by two examples based on the experimental measurements of the acoustic impedance and absorption of porous ceramic samples of different thicknesses and a sample of polyurethane foam. Słowa kluczowe: Acoustic modeling, Viscosity, Porous materials, Porous media, Acoustic impedance measurement Afiliacje autorów:
 25p.  
4.  Zieliński T.G., Generation of random microstructures and prediction of sound velocity and absorption for open foams with spherical pores, JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, ISSN: 00014966, DOI: 10.1121/1.4915475, Vol.137, No.4, pp.17901801, 2015 Streszczenie: This paper proposes and discusses an approach for the design and quality inspection of the morphology dedicated for sound absorbing foams, using a relatively simple technique for a random generation of periodic microstructures representative for opencell foams with spherical pores. The design is controlled by a few parameters, namely, the total open porosity and the average pore size, as well as the standard deviation of pore size. These design parameters are set up exactly and independently, however, the setting of the standard deviation of pore sizes requires some number of pores in the representative volume element (RVE); this number is a procedure parameter. Another pore structure parameter which may be indirectly affected is the average size of windows linking the pores, however, it is in fact weakly controlled by the maximal porepenetration factor, and moreover, it depends on the porosity and pore size. The proposed methodology for testing microstructuredesigns of sound absorbing porous media applies the multiscale modeling where some important transport parameters—responsible for sound propagation in a porous medium—are calculated from microstructure using the generated RVE, in order to estimate the sound velocity and absorption of such a designed material. Słowa kluczowe: Foams, Porous media, Viscosity, Acoustic absorption, Ceramics Afiliacje autorów:
 25p.  
5.  Nowak Ł.J., Zieliński T.G., Determination of the freefield acoustic radiation characteristics of the vibrating plate structures with arbitrary boundary conditions, JOURNAL OF VIBRATION AND ACOUSTICSTRANSACTIONS OF THE ASME, ISSN: 10489002, DOI: 10.1115/1.4030214, Vol.137, pp.05100118, 2015 Streszczenie: The paper presents the developed algorithm which implements the indirect variational boundary element method (IVBEM) for computation of the freefield acoustic radiation characteristics of vibrating rectangleshaped plate structures with arbitrary boundary conditions. In order to significantly reduce the computational time and cost, the algorithm takes advantage of simple geometry of the considered problem and symmetries between the elements. The procedure of determining the distribution of acoustic pressure is illustrated on the example of thin, rectangular plate with a part of one edge clamped and all other edges free. The eigenfrequencies and the corresponding vibrational mode shapes of the plate are computed using the finite element method (FEM). The results of the numerical simulations are compared to the results of the experiments carried out in an anechoic chamber, proving good agreement between the predictions and the observations. The reliability of simulations and high computational efficiency make the developed algorithm a useful tool in analysis of the acoustic radiation characteristics of vibrating plate structures. Słowa kluczowe: Acoustic radiation, Indirect variational Boundary Element Method, Plate structures Afiliacje autorów:
 25p.  
6.  Zieliński T.G., Microstructurebased calculations and experimental results for sound absorbing porous layers of randomly packed rigid spherical beads, JOURNAL OF APPLIED PHYSICS, ISSN: 00218979, DOI: 10.1063/1.4890218, Vol.116, No.3, pp.034905117, 2014 Streszczenie: Acoustics of stiff porous media with open porosity can be very effectively modelled using the socalled JohnsonChampouxAllardPrideLafarge model for sound absorbing porous media with rigid frame. It is an advanced semiphenomenological model with eight parameters, namely, the total porosity, the viscous permeability and its thermal analogue, the tortuosity, two characteristic lengths (one specific for viscous forces, the other for thermal effects), and finally, viscous and thermal tortuosities at the frequency limit of 0 Hz. Most of these parameters can be measured directly, however, to this end specific equipment is required different for various parameters. Moreover, some parameters are difficult to determine. This is one of several reasons for the socalled multiscale approach, where the parameters are computed from specific finiteelement analyses based on some realistic geometric representations of the actual microstructure of porous material. Such approach is presented and validated for layers made up of loosely packed small identical rigid spheres. The sound absorption of such layers was measured experimentally in the impedance tube using the socalled twomicrophone transfer function method. The layers are characterised by open porosity and semiregular microstructure: the identical spheres are loosely packed by random pouring and mixing under the gravity force inside the impedance tubes of various size. Therefore, the regular sphere packings were used to generate Representative Volume Elements suitable for calculations at the microscale level. These packings involve only one, two, or four spheres so that the threedimensional finiteelement calculations specific for viscous, thermal, and tortuous effects are feasible. In the proposed geometric packings, the spheres were slightly shifted in order to achieve the correct value of total porosity which was precisely estimated for the layers tested experimentally. Finally, in this paper some results based on the selfconsistent estimates are also provided. Słowa kluczowe: Viscosity, Porous media, Acoustic absorption, Acoustic modeling, Tensor methods Afiliacje autorów:
 30p.  
7.  Zieliński T.G., Potoczek M.^{♦}, Śliwa R.E.^{♦}, Nowak Ł.J., Acoustic absorption of a new class of alumina foams with various highporosity levels, ARCHIVES OF ACOUSTICS, ISSN: 01375075, DOI: 10.2478/aoa20130059, Vol.38, No.4, pp.495502, 2013 Streszczenie: Recently, a new class of ceramic foams with porosity levels up to 90% has been developed as a result of the association of the gelcasting process and aeration of the ceramic suspension. This paper presents and discusses original results advertising sound absorbing capabilities of such foams. The authors manufactured three types of alumina foams in order to investigate three porosity levels, namely: 72, 88, and 90%. The microstructure of foams was examined and typical dimensions and average sizes of cells (pores) and celllinking windows were found for each porosity case. Then, the acoustic absorption coefficient was measured in a wide frequency range for several samples of various thickness cut out from the foams. The results were discussed and compared with the acoustic absorption of typical polyurethane foams proving that the alumina foams with high porosity of 8890% have excellent sound absorbing properties competitive with the quality of sound absorbing PU foams of higher porosity. Słowa kluczowe: Sound absorption, Porous materials, Alumina foams Afiliacje autorów:
 20p.  
8.  Nowak Ł.J., Zieliński T.G., Modal sensitivity and selectivity of small, rectangleshaped piezoelectric transducers used as sensors and actuators in active vibroacoustic control systems, Journal of Low Frequency Noise, Vibration and Active Control, ISSN: 02630923, DOI: 10.1260/02630923.32.4.253, Vol.32, No.4, pp.253272, 2013 Streszczenie: The paper focuses on some issues regarding the utilization of small rectangleshaped piezoelectric transducers as both sensors and actuators in active vibration and vibroacoustic control systems of beam, plate and panelled structures with arbitrary (nonhomogeneous) boundary conditions. A new form of description of a simple proportional active control system with multiple independent feedback loops is proposed. The modal sensitivity functions of sensors and the modal selectivity functions of actuators are introduced to describe their ability for sensing and exciting specific structural modes of the structures. Basing on the assumed form of cost function and the derived equations of control system the influence of the modal characteristics of transducers on the stability of the system and on the performance of the active control is analyzed. The results of analytical solutions and numerical simulations are compared with the results of the experiments carried out on various beam and plate structures made up of aluminium or composite materials including the actual materials used in aviation, proving usefulness of the presented approach. Słowa kluczowe: Vibroacoustics, Piezoelectric transducers, Modal sensitivity, Vibroacoustic control systems Afiliacje autorów:
 15p.  
9.  Nowak Ł.J., Zieliński T.G., Meissner M., Active vibroacoustic control of plate structures with arbitrary boundary conditions, Prace IPPT  IFTR Reports, ISSN: 22993657, Vol.4a, pp.59, 2013 Streszczenie: The paper describes briefly some main aspects of the active feedback control system that has been developed and constructed for reduction of vibroacustic emission of vibrating plate structures with arbitrary boundary conditions. Relations between the forms and frequency of the vibrations induced by an external harmonic excitation and the distribution of the generated acoustic pressure field are investigated using the developed numerical model based on the Indirect Variational Boundary Element Method. The aim of the control is to minimize the sound pressure level in a given point of the ambient space. The system uses small, rectangleshaped piezoelectric transducers as both sensors and actuators. The transducers are connected in a number of independent feedback loops, and the feedback gains are the control parameters which are optimized using the developed optimal control algorithm. The constructed active system has been tested for the stability and control performance during experimental research performed in an anechoic chamber. Results of experiments are presented in the paper, proving a high level of noise reduction and a good agreement with numerical predictions. Słowa kluczowe: Vibrating plate structures, Active feedback control system, Vibrational modes Afiliacje autorów:
 
10.  Zieliński T.G., Galland M.A.^{♦}, Ichchou M.^{♦}, Fully coupled finiteelement modeling of active sandwich panels with poroelastic core, JOURNAL OF VIBRATION AND ACOUSTICSTRANSACTIONS OF THE ASME, ISSN: 10489002, DOI: 10.1115/1.4005026, Vol.134, No.2, pp.021007110, 2012 Streszczenie: Active sandwich panels are an example of smart noise attenuators and a realization of hybrid activepassive approach for the problem of broadband noise reduction. The panels are composed of thin elastic faceplates linked by the core of a lightweight absorbent material of high porosity. Moreover, they are active, so piezoelectric actuators in the form of thin patches are fixed to their faceplates. Therefore, the passive absorbent properties of porous core, effective at high and medium frequencies, can be combined with the active vibroacoustic reduction necessary in a low frequency range. Important convergence issues for fully coupled finiteelement modeling of such panels are investigated on a model of a diskshaped panel under a uniform acoustic load by plane harmonic waves, with respect to the important parameter of the total reduction of acoustic transmission. Various physical phenomena are considered, namely, the wave propagation in a porous medium, the vibrations of elastic plate and the piezoelectric behavior of actuators, the acousticsstructure interaction and the wave propagation in a fluid. The modeling of porous core requires the usage of the advanced biphasic model of poroelasticity, because the vibrations of the skeleton of porous core cannot be neglected; they are in fact induced by the vibrations of the faceplates. Finally, optimal voltage amplitudes for the electric signals used in active reduction, with respect to the relative size of the piezoelectric actuator, are computed in some lowertomedium frequency range. Słowa kluczowe: Active sandwich panels, Multiphysics, Vibroacoustics, Poroelasticity, Piezoelectricity Afiliacje autorów:
 20p.  
11.  Nowak Ł.J., Zieliński T.G., Acoustic radiation of vibrating plate structures submerged in water, HYDROACOUSTICS, ISSN: 16421817, Vol.15, pp.163170, 2012 Streszczenie: The paper presents results of the theoretical and numerical investigation on acoustic radiation of vibrating plate structures submerged in water. The current state of the art on the considered issues is briefly reviewed. Then, the method for determining eigenmode shape functions and eigenfrequencies of plate vibrating in water that has been used in presented study is introduced. The constitutive equations for solid domain and the pressure acoustic equation for liquid domain are coupled via boundary conditions and solved numerically using the finite element method. Structural mode shapes and eigenfrequencies computed for plate submerged in water are compared to analogous results obtained for air and for the in vacuo case. It is ssumed, that the plate is rectangle shaped and that it is placed in an infinite rigid baffle. Threedimensional near and farfield acoustic radiation characteristics for the plate vibrating in water are introduced. Possibilities of implementation of the active control system for reduction of the hydroacoustic emission are briefly discussed. Słowa kluczowe: Hydroacoustics, Plate structures, Hydrocoustic radiation Afiliacje autorów:
 4p.  
12.  Zieliński T.G., Numerical investigation of active porous composites with enhanced acoustic absorption, JOURNAL OF SOUND AND VIBRATION, ISSN: 0022460X, DOI: 10.1016/j.jsv.2011.05.029, Vol.330, pp.52925308, 2011 Streszczenie: The paper presents numerical analysis – involving an advanced multiphysics modeling – of the concept of active porous composite sound absorbers. Such absorbers should be made up of a layer or layers of poroelastic material (porous foams) with embedded elastic inclusions having active (piezoelectric) elements. The purpose of such active composite material is to significantly absorb the energy of acoustic waves in a wide frequency range, particularly, at lower frequencies. At the same time the total thickness of composite should be very moderate. The active parts of composites are used to adapt the absorbing properties of porous layers to different noise conditions by affecting the socalled solidborne wave – originating mainly from the vibrations of elastic skeleton of porous medium – to counteract the fluidborne wave – resulting mainly from the vibrations of air in the pores; both waves are strongly coupled, especially, at lower frequencies. In fact, since the traction between the air and the solid frame of porous medium is the main absorption mechanism, the elastic skeleton is actively vibrated in order to adapt and improve the dissipative interaction of the skeleton and air in the pores. Passive and active performance of such absorbers is analyzed to test the feasibility of this approach. Słowa kluczowe: Poroelasticity, Piezoelectricity, Active composites, Sound absorption, Finiteelement modelling Afiliacje autorów:
 30p.  
13.  Zieliński T.G., Rak M.^{♦}, Acoustic absorption of foams coated with MR fluid under the influence of magnetic field, JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, ISSN: 1045389X, DOI: 10.1177/1045389X09355017, Vol.21, pp.125131, 2010 Streszczenie: The article presents results of the acoustic measurements on opencell porous media coated with a magnetorheological (MR) fluid. Sound absorption of polyurethane foams of different, single and dual porosity was tested in the impedance tube. The measurements were conducted in three stages using clean samples, the same samples moistened with MR fluid, and finally, exposing the MR fluidcoated samples to a constant magnetic field. The transfer function method was employed to determine the acoustic absorption coefficient. Two significant, controllable effects were observed in the curve illustrating the variation of the acoustic absorption coefficient with frequency, especially, for the foams of dual porosity. Namely, relative to the fieldfree conditions, or to the clean foams, the most substantial peak in the absorption curve could be shifted by applying a magnetic field. Moreover, a resulting significant increase in acoustic absorption yields, in a wide frequency range directly behind the peak. Słowa kluczowe: Magnetorheological foams, Acoustic absorption, Adaptive sound insulator, Dualporosity foams Afiliacje autorów:
 27p.  
14.  Zieliński T.G., Multiphysics modeling and experimental validation of the active reduction of structureborne noise, JOURNAL OF VIBRATION AND ACOUSTICSTRANSACTIONS OF THE ASME, ISSN: 10489002, DOI: 10.1115/1.4001844, Vol.132, No.6, pp.061008114, 2010 Streszczenie: This paper presents a fully coupled multiphysics modeling and experimental validation of the problem of active reduction of noise generated by a thin plate under forced vibration. The plate is excited in order to generate a significant lowfrequency noise, which is then reduced by actuators in the form of piezoelectric patches glued to the plate with epoxy resin in locations singled out earlier during finite element (FE) analyses. To this end, a fully coupled FE system relevant for the problem is derived. The modeling is very accurate: The piezoelectric patches are modeled according to the electromechanical theory of piezoelectricity, the layers of epoxy resin are thoroughly considered, and the acousticstructure interaction involves modeling of a surrounding sphere of air with the nonreflective boundary conditions applied in order to simulate the conditions found in anechoic chamber. The FE simulation is compared with many experimental results. The sound pressure levels computed in points at different distances from the plate agree excellently with the noise measured in these points. Similarly, the computed voltage amplitudes of controlling signal turn out to be very good estimations. Słowa kluczowe: Lowfrequency noise reduction, Multiphysics modeling, Active structural acoustic control Afiliacje autorów:
 27p.  
15.  Zieliński T.G., Fundamentals of Multiphysics Modelling of PiezoPoroElastic Structures, ARCHIVES OF MECHANICS, ISSN: 03732029, Vol.62, No.5, pp.343378, 2010 Streszczenie: The paper discusses theoretical fundamentals necessary for accurate vibroacoustical modeling of structures or composites made up of poroelastic, elastic, and (active) piezoelectric materials, immersed in an acoustic medium (e.g. air). An accurate modeling of such hybrid activepassive vibroacoustic attenuators (absorbers or insulators) requires a multiphysics approach involving the finite element method to cope with complex geometries. Such fullycoupled, multiphysics model is given in this paper. To this end, first, the accurate PDEbased models of all the involved singlephysics problems are recalled and, since a mutual interaction of these various problems is of the uttermost importance, the relevant couplings are thoroughly investigated and taken into account in the modeling. Eventually, the Galerkin finite element model is developed. This model should serve to develop designs of active composite vibroacoustic attenuators made up of porous foams with passive and active solid implants, or hybrid liners and panels made up of a core or layers of porous materials fixed to elastic faceplates with piezoelectric actuators, and coupled to airgaps. A widespread design of such smart muffler s is still an open topic and should be addressed with accurate predictive tools based on the model proposed in the present paper. The model is accurate in the framework of kinematical and constitutive (material) linearity of behaviour. This is, however, the very case of the vibroacoustic application of elastoporoelastic panels or composites, where the structural vibrations are induced by acoustic waves. The developed fullycoupled FE model is finally used to solve a generic two dimensional example and some issues concerning finite element approximation and convergence are also discussed. Słowa kluczowe: Poroelasticity, Piezoelectricity, Acoustics, Multiphysics, Weak formulation, Finiteelement method Afiliacje autorów:
 27p.  
16.  Batifol C.^{♦}, Zieliński T.G., Ichchou M.^{♦}, Galland M.A.^{♦}, A finiteelement study of a piezoelectric/poroelastic sound package concept, SMART MATERIALS AND STRUCTURES, ISSN: 09641726, DOI: 10.1088/09641726/16/1/021, Vol.16, No.1, pp.168177, 2007 Streszczenie: This paper presents a complete finiteelement description of a hybrid passive/active sound package concept for acoustic insulation. The sandwich created includes a poroelastic core and piezoelectric patches to ensure high panel performance over the medium/high and low frequencies, respectively. All layers are modelled thanks to a Comsol environment*. The piezoelectric/elastic and poroelastic/elastic coupling are fully considered. The study highlights the reliability of the model by comparing results with those obtained from the Ansys finiteelement software and with analytical developments. The chosen shape functions and mesh convergence rate for each layer are discussed in terms of dynamic behaviour. Several layer configurations are then tested, with the aim of designing the panel and its hybrid functionality in an optimal manner. The differences in frequency responses are discussed from a physical perspective. Lastly, an initial experimental test shows the concept to be promising. Słowa kluczowe: Poroelasticity, Piezoelectricity, Finiteelement modelling, Acoustic insulation, Activepassive approach Afiliacje autorów:

Lista rozdziałów w ostatnich monografiach
1. 552  Meissner M., Zieliński T., Postępy Akustyki 2017, rozdział: Shape optimization of rectangular rooms for improving sound quality at low frequencies, Polskie Towarzystwo Akustyczne, Oddział Górnośląski, pp.461472, 2017  
2. 410  Zieliński T.G., GRAFEN – IPPT PAN COMPUTER OF BIOCENTRUM OCHOTA GRID, rozdział: Microstructurebased modelling of sound absorption in rigid porous media, IPPT Reports on Fundamental Technological Research, Postek E., Kowalewski T.A. (Eds.), pp.106111, 2014  
3. 364  Graczykowski C., Knor G., Kołakowski P., Mikułowski G., Orłowska A., Pawłowski P., Skłodowski M., Świercz A., Wiszowaty R., Zieliński T.G., Monitorowanie obciążeń i stanu technicznego konstrukcji mostowych, rozdział: Wybrane zagadnienia monitorowania, IPPT Reports on Fundamental Technological Research, pp.189236, 2014  
4. 199  Zieliński T.G., Smart technologies for safety engineering, rozdział: Modeling and analysis of smart technologies in vibroacoustics, Wiley, HolnickiSzulc J. (Ed.), pp.269321, 2008 
Prace konferencyjne
1.  Ahsani S.^{♦}, Deckers E.^{♦}, Zieliński T.G., Jankowski Ł., Claeys C.^{♦}, Desmet W.^{♦}, Absorption enhancement in poroelastic materials by mass inclusions, exploiting the massspring effect, SMART 2019, 9th ECCOMAS Thematic Conference on Smart Structures and Materials, 20190708/0711, Paris (FR), pp.10761084, 2019 Streszczenie: In this paper the possibility of enhancing the absorption coefficient of a poroelastic material using small, elastic mass inclusions in frequencies lower than the quarterwavelength resonance of the porous material is discussed. We show that absorption peaks can be achieved not only by what is known in literature as the trapped mode effect, but also by the resonance of small elastic inclusions at low frequencies, which can be interpreted as a massspring effect. In this work, the inclusion and the porous skeleton is considered elastic and fully coupled to each other, therefore accounting for all types of energy dissipation i.e. viscous, thermal, and structural losses and energy dissipated due to the relative motion of the fluid phase and the frame excited by the resonating inclusion. Additionally, the inclusions are also modeled as motionless and rigid to distinguish between the trapped mode and/or the modified frame mode effect and the massspring effect. Moreover, the distinction between these two effects are explained in more detail by comparing the dissipated energy by each mechanism (viscous, thermal and structural effect). Słowa kluczowe: Metaporous material, BiotAllard poroelastic model, Massspring effect Afiliacje autorów:
 
2.  Červenka M.^{♦}, Bednařík M.^{♦}, Zieliński T.G., Direct numerical simulation of sound absorption in porous media, Euronoise 2018  11th European Congress and Exposition on Noise Control Engineering, 20180527/0531, Hersonissos (GR), pp.5954, 2018 Streszczenie: Numerical simulation of absorption of sound in porous media is an important part of the design of the treatments for the environmental noise reduction. In the porous media, the mechanical energy carried by sound is dissipated by thermoviscous interactions with the solid surface of the media frame, which usually has complicated geometry at the microscopic (submillimetre) scale. In order to be able to absorb the acoustic energy at the low frequencies of interest, a layer of porous material must be rather thick (at the order of centimetres). This is why direct numerical simulation (DNS) of the sound absorption in porous media is a rather computationally challenging task because small geometrical details must be properly resolved in a large computational domain. In order to avoid these difficulties, simplified semiphenomenological models introducing so called effective fluid have been proposed. For example, the JohnsonChampouxAllardPrideLafarge (JCAPL) model is based on eight parameters which can be measured or calculated based on the media microstructural geometry. Within this work, we compare the numerical results obtained by the 3D DNS with the prediction of the JCAPL model in case of several porous media represented by closelypacked spheres. The DNS calculations are performed using the linearised NavierStokes equations for layers of spheres of different thicknesses, the parameters for the JCAPL model are calculated subsequently using Laplace, Poisson, and Stokes flow analyses on a representative volume element of the media. Very good agreement between the results has been found. Afiliacje autorów:
 
3.  Opiela K.C., Rak M.^{♦}, Zieliński T.G., A concept demonstrator of adaptive sound absorber/insulator involving microstructurebased modelling and 3Dprinting, ISMA 2018 / USD 2018, International Conference on Noise and Vibration Engineering / International Conference on Uncertainty in Structural Dynamics, 20180917/0919, Leuven (BE), pp.10911103, 2018 Streszczenie: The purpose of this work is to present and investigate the concept of adaptive sound absorbers, that is, periodic porous media with modifiable microgeometry, so that their ability of sound absorption or insulation can be changed in various frequency ranges. To demonstrate this concept, a simple periodic porous microgeometry with small bearing balls inside pores is proposed. By a simple positioning of the periodic porous sample the gravity force is used for the small balls to close some of the windows linking the pores, changing in that way the flow path inside pores, which entails significant modifications of the relevant parameters of permeability and tortuosity. Also the viscous characteristic length is changed, while the porosity as well as the thermal characteristic length remain unchanged. Nevertheless, such significant changes of some crucial transport parameters strongly affect the overall acoustic wave propagation in the porous medium. All this is studied using an advanced dualscale modelling as well as experimental testing of 3Dprinted specimens. Afiliacje autorów:
 
4.  Zieliński T.G., Galland M.A.^{♦}, Deckers E.^{♦}, Influencing the waveattenuating coupling of solid and fluid phases in poroelastic layers using piezoelectric inclusions and locally added masses, ISMA 2018 / USD 2018, International Conference on Noise and Vibration Engineering / International Conference on Uncertainty in Structural Dynamics, 20180917/0919, Leuven (BE), pp.11951207, 2018 Streszczenie: When airborne acoustic waves penetrate porous media their carrier becomes the air in pores, but also the solid skeleton  provided that it is sufficiently soft. Then, there is a coupled propagation of fluidborne and solidborne waves in a poroelastic medium. The coupling of fluid and solid phases of such media can be responsible for significantly better or weaker sound absorption in medium and lower frequency ranges. It has been observed that adding some welllocalised small mass inclusions inside a poroelastic layer may improve its acoustic absorption in some medium frequency range, however, at the same time the absorption is usually decreased at some slightly higher frequencies. This situation can be improved by applying additionally an active approach using small piezoelectric inclusions which actively influence the vibrations of the solid skeleton with added masses, so that the interaction between the solidborne and fluidborne waves is always directed for a better mutual energy dissipation of the both types of waves. Afiliacje autorów:
 
5.  Zieliński T.G., Poresize effects in sound absorbing foams with periodic microstructure: modelling and experimental verification using 3D printed specimens, ISMA 2016 / USD 2016, International Conference on Noise and Vibration Engineering / International Conference on Uncertainty in Structural Dynamics, 20160919/0921, Leuven (BE), pp.95104, 2016 Streszczenie: Microstructurebased modelling of sound absorbing porous media has been recently successfully applied for various materials, however, still some questions concerning the reliability and accuracy of such predictions are open. These issues are investigated here for periodic foams with open porosity. First, a geometry of foam microstructure is generated using an algorithm which ensures periodic arrangements of pores in a cube. Then, the cube is appropriately scaled to various sizes and for each size case finiteelement analyses are performed on the periodic fluid domain to calculate the socalled transport parameters. Finally, the effective speed of sound and density are determined for the socalled equivalent fluid, macroscopically suitable to describe wave propagation in such an open rigid foam filled with air. All this allows to estimate the sound absorption for periodic foam layers of various poresizes and thicknesses. This parametric study is confronted with some impedancetube measurements carried out for a few foam samples produced using 3Dprinting technology. Słowa kluczowe: Sound absorbing foams, Microstructure, Micromacro modelling, Acoustic testing, 3D printing Afiliacje autorów:
 15p.  
6.  Zieliński T.G., On representativeness of the representative cells for the microstructurebased predictions of sound absorption in fibrous and porous media, Euro Noise 2015, 10th European Congress and Exposition on Noise Control Engineering, 20150531/0603, Maastricht (NL), pp.24732478, 2015 Streszczenie: Realistic microstructurebased calculations have recently become an important tool for a performance prediction of sound absorbing porous media, seemingly suitable also for a design and optimization of novel acoustic materials. However, the accuracy of such calculations strongly depends on a correct choice of the representative microstructural geometry of porous media, and that choice is constrained by some requirements, like, the periodicity, a relative simplicity, and the size small enough to allow for the socalled separation of scales. This paper discusses some issues concerning this important matter of the representativeness of representative geometries (twodimensional cells or threedimensional volume elements) for sound absorbing porous and fibrous media with rigid frame. To this end, the accuracy of two and threedimensional cells for fibrous materials is compared, and the microstructurebased predictions of sound absorption are validated experimentally in case of a fibrous material made up of a copper wire. Similarly, the numerical predictions of sound absorption obtained from some regular Representative Volume Elements proposed for porous media made up of looselypacked identical rigid spheres are confronted with the corresponding analytical estimations and experimental results. Finally, a method for controlled random generation of representative microstructural geometries for sound absorbing open foams with spherical pores is briefly presented. Słowa kluczowe: Fibrous materials, Opencell foams, Representative microstructure, Modelling of sound absorption Afiliacje autorów:
 
7.  Zieliński T.G., A methodology for a robust inverse identification of model parameters for porous sound absorbing materials, ISMA 2014, International Conference on Noise and Vibration Engineering, 20140915/0917, Leuven (BE), pp.6376, 2014 Streszczenie: A methodology of inverse identification of parameters for the JohnsonChampouxAllardLafarge model of porous sound absorbing materials (also with Pride and Lafarge enhancements) is advocated. The inverse identification is based on the measurements of surface acoustic impedance of porous samples. For a single sample of porous material set on a rigid backing wall such measurements provide two specific curves in the considered frequency range, namely, the real and imaginary parts of acoustic impedance. More data suitable for inverse identification can be gathered from additional measurements where the surface acoustic impedance is determined for the same sample yet with an air gap between the sample and the backing wall. As matter of fact, such measurements should be carried out for a few cases where the air gap varies in thickness. Eventually, a set of impedance curves is gained suitable for inverse simultaneous identification of model parameters. In the paper analytical solutions are given for both measurement configurations, namely, for a layer of porous material set on the rigid wall, and for the porous layer separated from the rigid wall by an air gap. These solutions are used by the identification procedure which minimises the difference between the experimental curves and the curves computed from the analytical solutions where the porous layer is modelled using some version of the mentioned poroacoustic model. The minimisation is carried out with respect to the model parameters, however, not directly, since for this purpose the corresponding dimensionless parameters are introduced. Formulas for the dimensionless parameters are given with respect to the model parameters, and then conversely, for the model parameters with respect to the dimensionless ones. In the formulas two normalising frequencies are introduced which can be considered: one  as characteristic for viscous effects, and the other  as typical for thermal effects. It is claimed that they are not additional parameters, and can be set quite arbitrarily, however, reasonable values must be assumed to allow for very fast and robust identification with initial values for all dimensionless parameters set to 1. This feature is quite important in view of the fact that the choice of initial values for the actual model parameters is rather essential and can be often very problematic. The whole procedure is illustrated with a numerical example and by tests based on laboratory measurements of porous ceramic samples. Słowa kluczowe: Sound absorbing porous media, Inverse identification, Acoustic impedance, Acoustic testing Afiliacje autorów:
 10p.  
8.  Zieliński T.G., Sound absorption of porous layers of looselypacked rigid spheres: multiscale modelling and experimental validation, FA2014, 7th FORUM ACUSTICUM 2014, 20140907/0912, Kraków (PL), No.R13K_2, pp.16, 2014 Streszczenie: Sound absorption in porous media with rigid structure and open porosity is most often modelled using the socalled fluidequivalent approach, in which a porous medium is substituted by an effective dispersive fluid. There are many models of that kind. Perhaps the most frequently used and efficient one is the socalled JohnsonChampouxAllardLafrage model, or its variations. This a rather advanced semiphenomenological model with six to eight parameters; with enhancements by Pride and Lafarge, there are eight parameters, namely: the total open porosity, the tortuosity, the (viscous) permeability, the thermal permeability, the viscous and thermal characteristic lengths, and finally, the viscous and thermal tortuosities at low frequency limit (i.e., at 0 Hz). Although, most of these parameters can be measured, it is sometimes very problematic and requires various experimental facilities, which makes the idea of calculation of these parameters from the geometry of microstructure of porous medium very tempting – such multiscale modelling requires, however, some periodic yet sufficiently realistic representation of the actual porous geometry. In this paper such multiscale modelling is presented for the problem of sound absorption in layers composed of looselypacked rigid spheres. Since the spheres are identical, the packing, although not dense, tends to be semiregular. Therefore, some regular sphere packings are used to construct periodic Representative Volume Elements for such porous media – they are, however, modified a bit by shifting the spheres in order to fit exactly the actual measured porosity. Basing on such numerical representations of porous microstructure, all the necessary parameters are calculated from finiteelement solutions of some relevant BoundaryValue Problems and the effective characteristics for equivalent fluid are determined. Then, the acoustic absorption coefficients are computed for a porous layer of specified thickness for some wide frequency range and the results are compared with the experimental curve obtained from the measurements of such layer carried out in the impedance tube using the socalled twomicrophone transfer function method. Słowa kluczowe: Granular media, Sound absorption, Multiscale modelling, Acoustic measurements Afiliacje autorów:
 
9.  Zieliński T.G., Representative volume elements, microstructural calculation and macroscopic inverse identification of parameters for modelling sound propagation in rigid porous materials, ICSV20, 20th International Congress on Sound and Vibration: Recent Developments in Acoustics, Noise and Vibration, 20130707/0711, Bangkok (TH), pp.22282235, 2013 Streszczenie: The microgeometry of porous material is responsible for its sound absorption performance and should be now a design objective. Microstructural calculation of parameters and/or characteristic functions for acoustical models of porous materials with rigid frame requires the socalled Representative Volume Elements, that is, usually cubes which should contain several pores or fibres of typical sizes and distribution. The design of such RVEs, which correctly represent a typical microgeometry of porous medium, is by no means an easy task since usually the RVE should be also periodic and 'isotropic' (identical with respect to the three mutuallyperpendicular directions). The task is simpler in case of twodimensional microscopic models of some fibrous materials, but such modelling is obviously rather approximative. Designs of periodic RVEs for porous foams and fibrous materials will be presented and used by FE analyses of microstructural problems defined by the application of the Multiscale Asymptotic Method to the problem of sound propagation and absorption in porous media with rigid skeleton. Moreover, a methodology of automatic generation of periodic RVEs with random arrangement of pores based on a simple bubble dynamics will be explained. Among other examples, designs of RVE cubes representative for a corrundum ceramic foam with porosity 90% will be shown and serve for microstructural calculation of some macroscopic parameters used in advanced acoustical modelling of porous media. The curves of acoustic impedance and absorption measured in the frequency range from 500Hz to 6.4kHz for two samples of the corrundum foam will be presented. These measurements will be used for inverse identification of relevant macroscopic parameters, namely: the tortuosity, the viscous and thermal permeabilities, and two characteristic lengths. The concurrence of some results obtained by the RVEbased microscale calculation and the measurementbased macroscale identification will be shown. Słowa kluczowe: Rigid porous media, Microstructurebased calculations, Inverse identification, Sound propagation Afiliacje autorów:
 
10.  Nowak Ł.J., Zieliński T.G., Determining the optimal locations of piezoelectric transducers for vibroacoustic control of structures with general boundary conditions, ISMA 2012 / USD 2012, International Conference on Noise and Vibration Engineering / International Conference on Uncertainty in Structural Dynamics, 20120917/0919, Leuven (BE), pp.369383, 2012 Streszczenie: Vibroacoustic control of thin beam, plate and panelled structures with arbitrary boundary conditions is investigated. The study focuses on determining optimal locations of piezoelectric sensors and actuators on the surfaces of structures under vibroacoustic control. The work consists of three parts. In the first part, the undertaken assumptions and some governing equations are briefly introduced. Then, in the second part of the study, the piezotransducers' locations which ensure optimal sensing/actuating capabilities for specific vibration modes are determined, basing on the derived analytical formulas and on some results of numerical simulations, as well as on the actuator/sensor equations given in the first part of the study. The relevant modes are selected by taking into account that the main purpose is to minimise the acoustic field generated by the vibrating structure. The third part of the work discusses some experimental investigations aimed for the verification of the results obtained theoretically. Some technical aspects of creating the composite structures for active control systems are briefly described in appendix. Słowa kluczowe: Vibroacoustic panels, Vibroacoustic control, Piezoelectric transducers, Optimal placement Afiliacje autorów:
 10p.  
11.  Zieliński T.G., Inverse identification and microscopic estimation of parameters for models of sound absorption in porous ceramics, ISMA 2012 / USD 2012, International Conference on Noise and Vibration Engineering / International Conference on Uncertainty in Structural Dynamics, 20120917/0919, Leuven (BE), pp.95107, 2012 Streszczenie: Samples of porous ceramics Al2O3, manufactured by a promising technology of gelcasting of cellural foams by using biopolymers as gelformers, are examined in the impedance tube using the transfer function method. It is shown that the ceramics of total porosity around 90% forms an excellent sound absorbing material in the frequency range from 500 Hz to 6.4 kHz. Experimentallydetermined curves of acoustic impedance and absorption are then used for inverse identification of relevant geometric parameters like: tortuosity, viscous and thermal permeability parameters and characteristic lengths. These parameters are required by some advanced models of sound propagation in rigid porous media, developed by Johnson, Koplik and Dashen, Champoux and Allard, with some variations introduced by Pride et al., and Lafarge et al. These models are utilized to produce curves of acoustic impedance and absorption that are used by the identification procedure which minimizes the objective function defined as a squared difference to the appropriate curves obtained experimentally. As a matter of fact, some experimental data are used for the determination of parameters while the other dataobtained for another sample of the same porous ceramics, yet having different thicknessserve for the validation purposes. Moreover, it is observed that the identified characteristic length for thermal effects corresponds very well to the average radius of pores, whereas the characteristic length for viscous forces is similar with the average size of Słowa kluczowe: Soundabsorbing foams, Inverse identification, Microscale calculations, Porous ceramics Afiliacje autorów:
 10p.  
12.  Nowak Ł.J., Zieliński T.G., Wybrane aspekty aktywnej kontroli wibroakustycznej na przykładzie struktury płytowej, 58 Otwarte Seminarium z Akustyki, 20110813/0816, Jurata (PL), Vol.2, pp.129138, 2011 Streszczenie: W artykule przedstawiono wyniki badań nad aktywną redukcją transmisji wibroakustycznej przez strukturę płytową. Zakres przedstawionych w pracy zagadnień obejmuje zarówno opis teoretyczny rozpatrywanych zjawisk i układów, jak i rezultaty symulacji numerycznych oraz badań doświadczalnych. Rozważanym obiektem jest płyta aluminiowa o grubości 2mm z przyklejonymi na jednej z jej powierzchni elementami piezoelektrycznymi. Część tych elementów pełni funkcję sensorów, pozostałe zaś stanowią aktywatory, za pomocą których realizowane jest sterowanie aktywne. Kontroler pracuje w układzie sprzężenia zwrotnego, na jego wejście podawany jest wzmocniony i odwrócony w fazie sygnał napięciowy z sensorów, będący jednocześnie sygnałem błędu. Algorytm sterowania realizowany jest w oparciu o klasyczny regulator proporcjonalnocałkującoróżniczkujący (PID), dla różnych konfiguracji połączeń poszczególnych członów. Fizyczna realizacja kontrolera wykonana została w formie układu analogowego bazującego na niskoszumnych wzmacniaczach operacyjnych. Słowa kluczowe: Aktywna kontrola wibroakustyczna, Regulator PID, Aktywna redukcja drgań Afiliacje autorów:
 
13.  Zieliński T.G., Finiteelement modelling of fullycoupled active systems involving poroelasticity, piezoelectricity, elasticity, and acoustics, CMM 2011, 19th International Conference on Computer Methods in Mechanics, 20110509/0512, Warszawa (PL), pp.21818, 2011 Streszczenie: The paper discusses some issues concerning fullycoupled finiteelement modelling of activepassive systems for vibroacoustic attenuation, involving porous, piezoelectric, and elastic materials, as well as 'acoustic' (inviscid) fluids. For porous materials, the advanced, biphasic model of poroelasticity is used, which allows to consider elastic vibrations of solid skeleton important at lower frequencies and for porous composites with active inclusions. A discrete finiteelement model suitable for analysis of such multiphysics problems is briefly explained. The model is derived (using the Galerkin method) from the variational formulation of coupled problems of poroelasticity, piezoelectricity, elasticity, and acoustics. Finally, some relevant results obtained from a numerical analysis of a disk of active sandwich panel with poroelastic core, fitted into an acoustic waveguide, are presented. Słowa kluczowe: Acoustics, Porous media, Smart materials, Vibrations, Coupled fields, Finite element methods, Numerical analysis, Elasticity Afiliacje autorów:
 
14.  Zieliński T.G., Multiphysics modelling and experimental verification of active and passive reduction of structural noise, ICA 2010, 20th International Congress on Acoustics, 20100823/0827, Sydney (AU), pp.15, 2010 Streszczenie: A fullycoupled multiphysics modelling is applied for the problem of simultaneous active and passive reduction of noise generated by a thin panel under forced vibration providing many relevant results of various type (noise and vibration levels, necessary voltage for control signals, efficiency of the approach) which are validated experimentally. The panel is excited in order to generate a noise consisting of significant lower and higher frequency contributions. Then the lowfrequency noisy modes are reduced by actuators in the form of piezoelectric patches glued with epoxy resin in locations chosen optimally thanks to the multiphysics analysis, whereas the emission of higher frequency noise is attenuated by wellchosen thin layers of porous materials. To this end, a fullycoupled finite element system relevant for the problem is derived. Such multiphysics approach is accurate: advanced models of porous media are used for the porous layers, the piezoelectric patches are modelled according to the fullycoupled electromechanical theory of piezoelectricity, the layers of epoxy resin are thoroughly considered, finally, the acousticstructure interaction involves modelling of a surrounding sphere of air with the nonreflective boundary conditions applied in order to simulate the conditions found in anechoic chamber. The FE simulation is compared with many experimental results. The sound pressure levels computed in points at different distances from the panel agree excellently with the noise measured in these points. Similarly, the computed voltage amplitudes of controlling signal turn out to be very estimations. Słowa kluczowe: Structural acoustics and vibration, Active noise reduction, Poroelasticity, Sandwich panels Afiliacje autorów:
 
15.  Motylewski J., Pawłowski P., Rak M.^{♦}, Zieliński T.G., Identyfikacja źródeł aktywności wibroakustycznej maszyn metodą kształtowania wiązki sygnału (beamforming), XXXVII Ogólnopolskie Sympozjum Diagnostyka Maszyn, 20100308/0313, Wisła (PL), pp.18, 2010 Streszczenie: W zagadnieniach identyfikacji i lokalizacji źródeł aktywności wibroakustycznej maszyn, istotnym problemem jest wizualizacja pól rozkładu wielkości akustycznych na wybranych powierzchniach oraz określenie udziału poszczególnych źródeł w bilansie energetycznym sygnału wibroakustycznego maszyny. Słowa kluczowe: Wibroakustyka, Lokalizacja źródeł akustycznych, Beamforming Afiliacje autorów:
 
16.  Zieliński T.G., Active porous composites for wide frequencyrange noise absorption, ISMA 2008, International Conference on Noise and Vibration Engineering, 20080915/0917, Louvain (BE), Vol.1, pp.89103, 2008 Streszczenie: The paper presents a design, accurate multiphysics modeling and analysis of active porouscomposite sound absorbers. Such absorbers are made up of a layer of poroelastic material (a porous foam) with embedded elastic implants having active (piezoelectric) elements. The purpose of such active composite material is to significantly absorb the energy of acoustic waves in a wide frequency range, particularly, in low frequencies. At the same time the total thickness of composites should be very moderate. The active parts of composites are used to adapt the absorbing properties of porous layers to different noise conditions by affecting the socalled solidborne wave (originating mainly from the vibrations of elastic skeleton of porous medium) to counteract the fluidborne wave (resulting mainly from the vibrations of air in the pores); the both waves are strongly coupled, especially, in lower frequencies. Passive and active performance of the absorbers is analysed to test the feasibility of this approach. Słowa kluczowe: Poroelasticity, Piezoelectricity, Weak formulation, Acoustic insulation, Activepassive approach Afiliacje autorów:
 
17.  Zieliński T.G., Modelling of poroelastic layers with mass implants improving acoustic absorption, 19th International Congress on Acoustics, 20070902/0907, Madrid (ES), pp.18, 2007 Streszczenie: The paper presents the modelling and frequency analysis of poroelastic layers with heavy solid implants where an improvement of acoustic absorption at lower frequencies is observed. To model the porous material the Biot’s theory of poroelasticity is used while the solid implants are modelled in two ways: first, as small subdomains of elastic material (steel) situated inside the porouslayer, and for the second time, in a more virtual manner (mathematically equivalent to the presence of masses in the given points), as some adequate inertial terms added directly to the weak (variational) formulation of the problem. Since the solid implants are very small the both ways give similar results. Obviously, the second approach is much more efficient to carry out numerical tests where the influence of the distribution of masses for the acoustic absorption of layers can be analysed. It seems that the improvement by distributed masses (implants) may be greater than the one due to the mass effect alone. Słowa kluczowe: Poroelasticity, Weak formulation, Acoustic absorption Afiliacje autorów:
 
18.  Zieliński T.G., Galland M.A.^{♦}, Ichchou M.N.^{♦}, Further modeling and new results of active noise reduction using elastoporoelastic panels, ISMA 2006, International Conference on Noise and Vibration Engineering, 20060918/0920, Louvain (BE), Vol.1, pp.309319, 2006 Streszczenie: The paper presents further development in modeling of active elastoporoelastic sandwich panels. In fact, a new design of a demisandwich panel is proposed and analysed. A numerical model of panel is implemented in COMSOL Multiphysics environment using the most fundamental but very flexible Weak Form PDE Mode. Various physical problems are modeled using Finite Element Method: the wave propagation in acoustic and poroelastic medium, the vibrations of elastic plate, the piezoelectric behavior of actuator. All these problems interact. in the examined application of active panel. The presented results of FE analysis and some analytical solutions prove the necessity of modeling the panel's interaction with an acoustic medium. Again, confirmed is the fact that an active control is necessary for lower resonances while for the higher frequencies the passive reduction of vibroacoustic transmission performed by a welldesigned poroelastic layer is sufficient. Słowa kluczowe: Active sandiwch panels, Poroelasticity, Piezoelectricity, Vibroacoustics Afiliacje autorów:
 
19.  Zieliński T.G.^{♦}, Galland M.A.^{♦}, Ichchou M.^{♦}, Active reduction of vibroacoustic transmission using elastoporoelastic sandwich panels and piezoelectric materials, SAPEM'2005, Symposium on the Acoustics of PoroElastic Materials, 20051207/1209, Lyon (FR), pp.18, 2005 Streszczenie: The paper addresses the issue of an active sandwich panel made of elastic faceplates and a poroelastic core. The panel is supposed to be active thanks to piezoelectric patches glued to the one of elastic layers. This piezoelectric actuator is used to excite the panel vibrations in the low frequency range with the aim to reduce the transmitted wave. A complete description of the sandwich behaviour is obtained using a finite element model implemented in FEMLAB environment. The poroelastic material is modeled using a recent formulation (by Atalla et al.) valid for harmonic oscillations, but the classical Biot formulation is also implemented. Coupling occurring between poroelastic material and plates, and between elastic plate and piezoelectric patches is fully considered. The achieved numerical model allows prediction of transmission coefficient for plane waves under normal incidence. Hence, some numerical experiments can be offered for multiple assembly configurations whose ultimate goal is to determine the best assembly and the best control strategy for reducing the transmission over a wide frequency range. Słowa kluczowe: Poroelacticity, Piezoelectricity, Active vibroacoustic panles Afiliacje autorów:

Abstrakty konferencyjne
1.  Zieliński T.G., Opiela K.C., Multiscale and multiphysics modelling of an adaptive material for sound absorption, COMSOL CONFERENCE, 20181022/1024, Lausanne (CH), pp.12, 2018  
2.  Zieliński T.G., Jankowski Ł., Opiela K., Deckers E.^{♦}, Modelling of poroelastic media with localised mass inclusions, SAPEM'2017, SAPEM'2017  5th Symposium on the Acoustics of PoroElastic Materials, 20171206/1208, Le Mans (FR), pp.12, 2017  
3.  Zieliński T.G., Multiphysics modelling of sound absorbing fibrous materials, COMSOL 2015, COMSOL Conference, 20151014/1016, Grenoble (FR), pp.13, 2015 Streszczenie: Many of fibrous materials are very good sound absorbers, because the acoustic waves, which propagate in air and penetrate a fibrous layer, interact with the fibres so that the wave energy is dissipated. The dissipation is related to some viscous and thermal effects occurring on the microscale level. On the macroscopic level, a fibrous medium can be treated as an effective inviscid fluid, provided that the fibres are stiff. Such a fluidequivalent approach allows to use the Helmholtz equation for the macroscopic description of sound propagation and absorption. It is applied by the advanced JohnsonAllard models, which require from 5 to 8 parameters related to the microgeometry of fibrous microstructure. These are the socalled transport parameters in porous media: the open porosity and tortuosity, the permeability and its thermal analogue, two characteristic lengths (for viscous forces and thermal effects), etc. Moreover, some parameters for air (which fills the medium) are also necessary. Słowa kluczowe: Fibrous materials, Sound absorption, Multiphysics modelling Afiliacje autorów:
 
4.  Zieliński T.G., Multiscale modelling of the acoustic waves in rigid porous and fibrous materials, PCMCMM 2015, 3rd Polish Congress of Mechanics and 21st Computer Methods in Mechanics, 20150908/0911, Gdańsk (PL), pp.601602, 2015 Streszczenie: This paper presents the multiscale approach to the problem of acoustic waves propagating in a fluid (air) inside rigid fibrous of porous materials with open porosity. The approach essentially consists of the finite element analyses of three relevant problems defined on the representative fluid domain of a porous medium, the averaging and upscaling techniques applied to calculate some necessary parameters from the porous microstructure which are used by a model for the effective properties of a homogenized fluid equivalent to the porous medium, and finally, the solution of a relevant Helmholtz problem on the macroscale level in order to estimate, for example, the acoustic absorption of the porous medium. In the paper, this approach is illustrated by two examples: experimentally validated analyses of a fibrous material made up of a copper wire based on two Representative Volume Elements, and an analysis of a foam with spherical pores using a randomly generated periodic representative cell. Słowa kluczowe: Multiscale modelling, Acoustic waves, Porous media, Fibrous materials Afiliacje autorów:
 
5.  Zieliński T.G., Microstructure generation for design of sound absorbing foams with spherical pores, SAPEM'2014, Symposium on the Acoustics of PoroElastic Materials, 20141216/1218, Stockholm (SE), pp.12, 2014 Streszczenie: The paper presents an approach for a morphological design of foams with spherical pores. It involves an algorithm for random generation of foam microstructure (controlled by some parameters), which is used to compute the transport parameters, and then, the effective speed of sound. Eventually, the sound absorption of such designed foam can be estimated. Słowa kluczowe: Foams with spherical pores, Microstructure design, Sound absorption, Micromacro modelling Afiliacje autorów:
 
6.  Zieliński T.G., Multiphysics modelling of sound absorption in rigid porous media based on periodic representations of their microstructural geometry, COMSOL 2013, COMSOL Conference, 20131023/1025, Rotterdam (NL), pp.13, 2013 Streszczenie: Sound absorption in porous materials with rigid frame and open porosity can be very effectively estimated by applying the JohnsonAllard model in order to substitute a porous medium with an equivalent effective fluid and then utilise the Helmholtz equation for timeharmonic acoustics. The model uses several parameters which characterize the microgeometry of porous material from the macroscopic perspective; they are: the total porosity, the viscous permeability and its thermal analogue, the tortuosity, and two characteristic lengths  one specific for viscous forces, the other for thermal effects. These parameters can be measured experimentally, however, recent computational powers allow to calculate them from the microstructure of porous medium provided that a good representation of usually very complex microgeometry can be found. Inverse identification of these parameters is also possible. Słowa kluczowe: Multiphysics modelling, Rigid porous media, Sound absorption Afiliacje autorów:
 
7.  Zieliński T.G., Concurrence of the microscale calculation and inverse identification of parameters used for modelling acoustics of porous media, SolMech 2012, 38th Solid Mechanics Conference, 20120827/0831, Warszawa (PL), pp.216217, 2012 Streszczenie: There are several widelyused acoustic models of porous media, starting from that simple, purely phenomenological, model proposed by Delany and Bazely, and finishing with semiphenomenological propositions of Johnson et al., combined with the ones of Champoux and Allard, with some important variations proposed by Pride, Lafarge, and others. All these models use some average macroscopic parameters, namely: the total porosity and flow resistivity (or permeability)  for the DelanyBazely model  which are supplemented by the average tortuosity of pores and their characteristic dimensions  in the case of more advanced semiphenomenological models. These models allow to describe the acoustic wave propagation in porous media in a wide frequency range, provided that the skeleton is rigid. However, using some formulas derived for these models with the Biot’s theory of poroelasticity permits to describe correctly sound propagation in soft porous materials. Thus, the determination of the abovementioned parameters is very important. For direct, experimental measurements specialistic equipment is required, different for various parameters. Therefore, an inverse identification based on curves of, for example, acoustic impedance or absorption (measured for samples of known thickness) can be used to estimate the model parameters. In this work, it will be shown that knowledge of microstructural geometry of porous medium is very helpful to validate correct estimation. Moreover, a periodic microscopic cell consisting of a few pores representing an average morphology of porous ceramics is proposed to serve for numerical analyses to estimate permeability parameters. The concurrence of such microscale derivation and inverse identification is discussed. Słowa kluczowe: Porous media, Microscale calculations, Inverse indentification, Sound waves Afiliacje autorów:
 
8.  Nowak Ł.J., Zieliński T.G., Active vibroacoustic control of beams and plates with general boundary conditions, SolMech 2012, 38th Solid Mechanics Conference, 20120827/0831, Warszawa (PL), pp.294295, 2012 Streszczenie: Active vibroacoustic control of beam and plate structures with arbitrary boundary conditions is considered. The goal is to develop a method of minimizing sound radiation efficiency of such structures. Primary sound field arise as a result of vibrations, due to external disturbances. It is assumed that the control system is compact  it does not contain any additional, ambient microphones. Piezoelectric transducers, mounted on the surface of the controled object, are used as sensors and actuators. Accurate numerical model of the considered structure is needed to determine optimal parameters of the control system. Theoretical background and the results of numerical and experimental research are briefly introduced. Słowa kluczowe: Active vibroacoustic control, Plate structures, Beams, Piezoelectric transducers Afiliacje autorów:
 
9.  Zieliński T.G., Porous foams with active implants improving acoustic absorption, SAPEM'2008, Symposium on the Acoustics of PoroElastic Materials, 20081217/1219, Bradford (GB), pp.14, 2008 Streszczenie: The paper presents an accurate multiphysics modeling and analysis of active porouscomposite sound absorbers composed of a layer of poroelastic material (a porous foam) with embedded elastic implants having active (piezoelectric) elements. The purpose of such active composite material is to significantly absorb the energy of acoustic waves in a wide frequency range. At the same time the total thickness of composites should be very small. The active parts of composites are used to adapt the absorbing properties of porous layers to different noise conditions by affecting the socalled solidborne wave (originating mainly from the vibrations of elastic skeleton of porous medium) to counteract the fluidborne wave (resulting mainly from the vibrations of air in the pores); the both waves are strongly coupled, especially, in lower frequencies. Passive and active performance of the absorbers is analysed to test the feasibility of this approach. Since the absorption should be actively improved by affecting the vibrations of the elastic skeleton of porous layers, it is apparent that the rigidframe modelling cannot be used here. Instead, the advanced biphasic theory of poroelasticity must be used to model porous material of the active absorbers. Słowa kluczowe: Poroelasticity, Active piezoelectric inclusions, Smart materials, Acoustic absorption Afiliacje autorów:
