Assoc. Prof. Mirosław Meissner, Ph.D., Dr. Habil., Eng.

Department of Intelligent Technologies (ZTI)
Division of Intelligent Systems (ZeSI)
position: professor IPPT
telephone: (+48) 22 826 12 81 ext.: 317
room: 124
e-mail: mmeissn

Doctoral thesis
1990Generacja dźwięku o dyskretnej częstotliwości przy opływie wnęki głębokiej przez strumień gazu 
supervisor -- Prof. Zbigniew Wesołowski, Ph.D., Dr. Habil., Eng., IPPT PAN
466 
Habilitation thesis
2000Badania odpowiedzi układów rezonansowych na pobudzenie akustyczne i aerodynamiczne 
Supervision of doctoral theses
1.2014-11-27Nowak Łukasz  Adaptive feedback control system for reduction of vibroacoustic emission671
 
2.2012-10-04Raunmiagi Zygmunt  
(AM)
Metoda oceny stanu powierzchni stożkowych rozpylaczy paliwa silników okrętowych za pomocą emisji akustycznej1081
 

Recent publications
1.Meissner M., Acoustics of small rectangular rooms: Analytical and numerical determination of reverberation parameters, APPLIED ACOUSTICS, ISSN: 0003-682X, DOI: 10.1016/j.apacoust.2017.01.020, Vol.120, pp.111-119, 2017
Abstract:

A small rectangular room with hard walls has a number of acoustic flaws and the most serious drawback is a long reverberation time. A technique commonly used for improving room acoustics consists in increasing a sound absorption on a ceiling. In this study, the impact of acoustical treatment of a ceiling on reverberant properties of a small rectangular room was examined. Changes in the modal reverberation time due to this treatment were investigated by the analytical method. As was evidenced by calculations, the initial increase in a sound absorption on a ceiling causes a substantial decrease in the modal reverberation time and a treatment efficiency decreases with a further absorption increase. It was found also that for a room with hard walls statistical and wave theories give the same result as the modal reverberation time for oblique modes and the Sabine’s reverberation time are identical. A more detailed information about reverberant properties of a room was provided by the numerical method employing a backward integration of the squared room impulse response. Using this method, global and local reverberation parameters were determined. Numerical simulations discovered a quite good agreement between global and local reverberation time and high differences between global and local early decay time resulting from a nonlinear shape of a decay curve. Therefore, one can conclude that the global decay times characterize reasonably well a reverberation process in a late stage of sound decay but they are not correctly describe this process in an initial stage.

Keywords:

Small room acoustics, Modal expansion method, Room impulse response, Reverberation time, Early decay time

Affiliations:
Meissner M.-IPPT PAN
2.Meissner M., Prediction of Reverberant Properties of Enclosures via a Method Employing a Modal Representation of the Room Impulse Response, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, DOI: 10.1515/aoa-2016-0003, Vol.41, No.1, pp.27-41, 2016
Abstract:

A theoretical method has been presented to describe sound decay in enclosures and simulate the room impulse response (RIR) employed for prediction of the indoor reverberation characteristics. The method was based on a solution of wave equation with the form of a series whose time-decaying components represent responses of acoustic modes to an impulse sound source. For small sound absorption on room walls this solution was found by means of the method of variation of parameters. A decay function was computed via the time-reverse integration of the squared RIR. Computer simulations carried out for a rectangular enclosure have proved that the RIR function reproduces the structure of a sound field in the initial stage of sound decay sufficiently well. They have also shown that band-limitedness of the RIR has evident influence on the shape of the decay function and predicted decay times.

Keywords:

room acoustics, indoor reverberation, room impulse response, modal expansion method, decay times

Affiliations:
Meissner M.-IPPT PAN
3.Meissner M., Numerical investigation of acoustic field in enclosures: Evaluation of active and reactive components of sound intensity, JOURNAL OF SOUND AND VIBRATION, ISSN: 0022-460X, DOI: 10.1016/j.jsv.2014.10.043, Vol.338, pp.154-168, 2015
Abstract:

The paper focuses on a theoretical description and numerical evaluation of active and reactive components of sound intensity in enclosed spaces. As the study was dedicated to low-frequency room responses, a modal expansion of the sound pressure was used. Numerical simulations have shown that the presence of energy vortices whose size and distribution depend on the character of the room response is a distinctive feature of the active intensity field. When several modes with frequencies close to a source frequency are excited, the vortices within the room are positioned irregularly. However, if the response is determined by one or two dominant modes, a regular distribution of vortices in the room can be observed. The irrotational component of the active intensity was found using the Helmholtz decomposition theorem. As was evidenced by numerical simulations, the suppression of the vortical flow of sound energy in the nearfield permits obtaining a clear image of the sound source.

Keywords:

room acoustics, modal analysis, sound intensity, energy vortex, stagnation point

Affiliations:
Meissner M.-IPPT PAN
4.Meissner M., Theoretical and Numerical Determination of Low-Frequency Reverberant Characteristics of Coupled Rooms, JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME, ISSN: 1048-9002, DOI: 10.1115/1.4029991, Vol.137, No.4, pp.041013-1-9, 2015
Abstract:

The main aim of room acoustics is to predict reverberant properties of enclosures from measured or numerically simulated room responses. In this paper, this issue was examined in low-frequency range where acoustic characteristics of rooms are strongly frequency dependent due to differences in a modal damping. A theoretical description of a decaying sound field was based on a modal expansion of the sound pressure, and a reverberant response of the room was initiated by emission of Dirac delta time impulse or by switching off a time-harmonic source. Theoretical findings were employed to determine reverberant characteristics of a coupled-room system containing two connected rectangular subrooms. Simulation results have shown that a sound decay after steady-state harmonic excitation is strongly influenced by the sound frequency and due to large fluctuations in a decaying pressure; numerical techniques for smoothing decay curves are needed. Calculations also revealed that in some one-third octave bands, the decay function found via backward integration of squared room impulse response (RIR) changes very irregularly impeding a proper qualifying of nature of sound decay.

Keywords:

room acoustics, modal analysis, decay times, coupled rooms

Affiliations:
Meissner M.-IPPT PAN
5.Meissner M., Sound Energy Field in a System of Coupled Rooms, ACTA PHYSICA POLONICA A, ISSN: 0587-4246, DOI: 10.12693/APhysPolA.125.A-103, Vol.125, No.4A, pp.A-103-A-107, 2014
Abstract:

The paper presents a theoretical basis of calculations of the sound intensity in enclosed spaces and shows results of numerical visualization of the active intensity in a room with absorptive walls formed by two coupled rectangular subrooms. The study was focused on the low-frequency range, therefore to describe the active and reactive intensities, the modal theory of room acoustics was applied. Space distribution of eigenfunctions, modal frequencies and modal damping coefficients were calculated numerically using the forced oscillator method (FOM) and the nite difference time-domain (FDTD) method. Based on theoretical and numerical results, the computer program has been developed to simulate the active intensity vector eld when the room is excited by a harmonic point source. Calculation data have shown that the active intensity was extremely sensitive to position of the source since at a fixed source frequency, different source locations always generate different distributions of characteristic objects of the active sound eld such as energy vortices and stagnation points. Because of complex room shape, the vortex centers are in most cases positioned irregularly inside the room. Almost regular arrangement of vortices was found only in the case when the source frequency was tuned to the frequencies of modes which were strongly localized in one of the subrooms.

Keywords:

room acoustics, coupled rooms, sound intensity, energy vortex, stagnation point

Affiliations:
Meissner M.-IPPT PAN
6.Meissner M., Analytical and numerical study of acoustic intensity field in irregularly shaped room, APPLIED ACOUSTICS, ISSN: 0003-682X, DOI: 10.1016/j.apacoust.2012.11.009, Vol.74, No.5, pp.661-668, 2013
Abstract:

The modal expansion method has been used to formulate expressions for real and imaginary parts of the complex sound intensity inside enclosures. Based on theoretical results, the computer program has been developed to simulate the acoustic intensity vector field inside the irregular room whose shape resembles the capital letter L. Calculation results have shown that a low-frequency distribution of the acoustic intensity is strongly influenced by the modal localization and the characteristic objects in the active intensity field are energy vortices and saddle points positioned irregularly inside the room. It was found that for small sound damping the vortex centers lie exactly on the lines corresponding to zeros of the eigenfunction for a dominant mode. An increase in a sound attenuation results in the change of vortex positions and can cause the formation of new vortices. Finally, an influence of the wall impedance on the quantitative relation between the acoustic and reactive intensities was studied and it was concluded that for very small sound damping the behavior of the sound intensity is basically only oscillatory.

Keywords:

Room acoustics, Irregular room, Sound intensity, Energy vortex, Modal localization

Affiliations:
Meissner M.-IPPT PAN
7.Meissner M., Acoustic Behaviour of Lightly Damped Rooms, ACTA ACUSTICA UNITED WITH ACUSTICA, ISSN: 1610-1928, DOI: 10.3813/AAA.918663, Vol.99, No.5, pp.845-847, 2013
Abstract:

The analytical method has been developed to determine the acoustic behaviour of a lightly damped room excited by a sound source. Using the classical modal analysis, a solution of the wave equation was found as a sum of an infinite number of components representing individual responses of acoustic modes to the sound source. For weak sound absorption a general form of this solution was determined by means of the method of variation of parameters. From this solution the equations for the Green's function and the room impulse response were found. By employing the Green's function, the expressions describing a sound build-up and a sound decay for a harmonic excitation were derived.

Keywords:

room acoustics, wave equation, room impulse response, decay times

Affiliations:
Meissner M.-IPPT PAN
8.Meissner M., Evaluation of Decay Times from Noisy Room Responses with Pure-Tone Excitation, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, DOI: 10.2478/aoa-2013-0006, Vol.38, No.1, pp.47-54, 2013
Abstract:

Reverberant responses are widely used to characterize acoustic properties of rooms, such as the early decay time (EDT) and the reverberation times T20 and T30. However, in real conditions a sound decay is often deformed by background noise, thus a precise evaluation of decay times from noisy room responses is the main problem. In this paper this issue is examined by means of numerical method where the decay times are estimated from the decay function that has been determined by nonlinear polynomial regression from a pressure envelope obtained via the discrete Hilbert transform. In numerical experiment the room responses were obtained from simulations of a sound decay for two-room coupled system. Calculation results have shown that background noise slightly affects the evaluation of reverberation times T20 and T30 as long as the signal-to-noise ratio (SNR) is not smaller than about 25 and 35 dB, respectively. However, when the SNR is close to about 20 and 30 dB, high overestimation of these times may occur as a result of bending up of the decay curve during the late decay.

Keywords:

room acoustics, reverberation, decay times, room response, background noise, coupled rooms

Affiliations:
Meissner M.-IPPT PAN
9.Nowak Ł.J., Zieliński T.G., Meissner M., Active vibroacoustic control of plate structures with arbitrary boundary conditions, IPPT REPORTS, ISSN: 2299-3657, Vol.4a, pp.5-9, 2013
Abstract:

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, rectangle-shaped 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.

Keywords:

Vibrating plate structures, Active feedback control system, Vibrational modes

Affiliations:
Nowak Ł.J.-IPPT PAN
Zieliński T.G.-IPPT PAN
Meissner M.-IPPT PAN
10.Meissner M., Acoustic energy density distribution and sound intensity vector field inside coupled spaces, JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, ISSN: 0001-4966, Vol.132, No.1, pp.228-238, 2012
Abstract:

In this paper, the modal expansion method supported by a computer implementation has been used to predict steady-state distributions of the potential and kinetic energy densities, and the active and reactive sound intensities inside two coupled enclosures. The numerical study was dedicated to low-frequency room responses. Calculation results have shown that the distribution of energetic quantities in coupled spaces is strongly influenced by the modal localization. Appropriate descriptors of the localization effect were introduced to identify localized modes. As was evidenced by numerical data, the characteristic objects in the active intensity field are vortices positioned irregularly inside the room. It was found that vortex centers lie exactly on the lines corresponding to zeros of the eigenfunction for a dominant mode. Finally, an impact of the wall impedance on the quantitative relationship between the active and reactive intensities was analyzed and it was concluded that for very small sound damping the behavior of the sound intensity inside the room space is essentially only oscillatory.

Keywords:

room acoustics, coupled rooms, acoustic energy density, active sound intensity, reactive sound intensity

Affiliations:
Meissner M.-IPPT PAN
11.Meissner M., The discrete Hilbert transform and its application to the analysis of reverberant decay of modal vibration in enclosures, JOURNAL OF VIBRATION AND CONTROL, ISSN: 1077-5463, DOI: 10.1177/1077546311420896, Vol.18, pp.1595-1606, 2012
Abstract:

The Hilbert transform is an important tool for a signal analysis, and it has been widely used in many areas of science and technology. An application of this method to an analysis of reverberant decay of modal vibrations in enclosures enables a detection of a pressure envelope resulting in a more accurate prediction of a reverberation time. It is shown that the discrete Hilbert transform is not accurate in an envelope detection even for the moderately damped harmonic signals, and a generated error strongly depends on the ratio of a modal damping coefficient to a mode frequency. This inexactness is due to the fact that for exponentially decaying harmonic signals the Bedrosian identity is not satisfied. In order to increase the accuracy of the envelope prediction, appropriate modifications of discrete signals corresponding to different kinds of modes are proposed. This method is successfully tested in the multi-mode case using discrete signals simulating a reverberant response of two coupled rooms.

Keywords:

Hilbert transform, modal vibrations, reverberation time, room acoustics

Affiliations:
Meissner M.-IPPT PAN
12.Meissner M., Accuracy issues of discrete Hilbert transform in identification of instantaneous parameters of vibration signals, ACTA PHYSICA POLONICA A, ISSN: 0587-4246, Vol.121, No.1-A, pp.A-164-167, 2012
Abstract:

In the paper, an accuracy of the discrete Hilbert transform method in a detection of amplitude and frequency of vibration signals has been examined. This issue was studied for sinusoidal damped vibrations often encountered in practical applications. It has been shown that an inexactness of the Hilbert transform generates fictitious oscillations of amplitude and frequency. For small damping of vibrations these oscillations were significant only at both ends of a discrete signal. An error induced by a numerical algorithm was especially severe for strongly damped vibrations because it manifested itself by a large overestimation of amplitude and erroneous jumps of frequency. To reduce the error generated by the Hilbert transform method, the appropriate modification of discrete signal was proposed.

Keywords:

vibration signals, discrete Hilbert transform, Bedrosian theorem

Affiliations:
Meissner M.-IPPT PAN
13.Meissner M., Numerical modelling of coupled rooms: evaluation of decay times via method employing Hilbert transform, ACTA PHYSICA POLONICA A, ISSN: 0587-4246, Vol.119, pp.1031-1034, 2011
Abstract:

In the paper, a usefulness of the Hilbert transform in a computer modelling of reverberant behaviour of rooms is demonstrated for the enclosure consisting of two coupled subrooms. In numerical simulations a decay of the sound pressure is computed and the Hilbert transform methodology is used to determine an envelope of this decay. Calculation results have shown that, because of the mode localization, a distribution of absorbing material has a great influence on decay times evaluated from changes in the pressure envelope. For example, when a difference between the sound damping in subrooms is large, the localization effect is responsible for a creation of a nonlinear decay of the sound pressure level characterized by rapid early and slow late sound decays.

Keywords:

room acoustics, reverberant behaviour of rooms, coupled rooms, Hilbert transform

Affiliations:
Meissner M.-IPPT PAN
14.Meissner M., Examination of the effect of a sound source location on the steady-state response of a two-room coupled system, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.36, pp.761-775, 2011
Abstract:

In this paper, the computer modelling application based on the modal expansion method is developed to study the influence of a sound source location on a steady-state response of coupled rooms. In the research, an eigenvalue problem is solved numerically for a room system consisting of two rectangular spaces connected to one another. A numerical procedure enables the computation of shape and frequency of eigenmodes, and allows one to predict the potential and kinetic energy densities in a steady-state. In the first stage, a frequency room response for several source positions is investigated, demonstrating large deformations of this response for strong and weak modal excitations. Next, a particular attention is given to studying how the changes in a source position influence the room response when a source frequency is tuned to a resonant frequency of a strongly localized mode.

Keywords:

coupled room system, steady-state room response, potential and kinetic energy densities, localization of modes

Affiliations:
Meissner M.-IPPT PAN
15.Meissner M., Simulation of acoustical properties of coupled rooms using numerical technique based on modal expansion, ACTA PHYSICA POLONICA A, ISSN: 0587-4246, Vol.118, No.1, pp.123-127, 2010
Abstract:

In the present study, the acoustic characteristics of coupled rooms were investigated using the computer modelling application based on the modal expansion method. A numerical procedure enables the computation of shape and frequency of eigenmodes, and allows one to predict sound decay times at any point of a room space. Results of numerical simulation have shown that along with a change in a coupling area the effect of a mode degeneration appeared and there are two main reasons for this. First, a mode degeneration is associated with a convergence of frequencies of neighbouring modes with a decrease of coupling area. Another reason for the mode degeneration are variations in a sequence of modes with a change in the coupling area. It was demonstrated that in the coupled rooms several modes exhibit a considerable localization. A degree of mode localization was described theoretically by the “existence surface” of mode and it was found that the localization phenomenon has a great effect on the reverberation process because for some absorbing material distributions it caused the double–slope decay characterized by steep initial and slow late sound decays.

Affiliations:
Meissner M.-IPPT PAN
16.Meissner M., Effect of cross-sectional area discontinuities in closed hard-walled duct on frequency of longitudinal modes, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.35, No.3, pp.421-435, 2010
Abstract:

A simple analytical method is developed to estimate frequencies of longitudinal modes in closed hard-walled ducts with discontinuities in a cross-sectional area. The approach adopted is based on a general expression for the acoustic impedance for a plane wave motion in a duct and conditions of impedance continuity at duct discontinuities. Formulae for mode frequencies in a form of transcendental equations were found for one, two and three discontinuities in a duct cross-section. An accuracy of the method was checked by a comparison of analytic predictions with calculation data obtained by use of numerical implementation based on the forced oscillator method with a finite difference algorithm.

Keywords:

longitudinal duct modes, discontinuity in duct cross-section, contraction ratio

Affiliations:
Meissner M.-IPPT PAN
17.Meissner M., Spectral characteristics and localization of modes in acoustically coupled enclosures, ACTA ACUSTICA UNITED WITH ACUSTICA, ISSN: 1610-1928, DOI: 10.3813/AAA.918152, Vol.95, No.2, pp.300-305, 2009
Abstract:

In this paper spectral characteristics and a mode localization in acoustically coupled enclosures were studied numerically. In a theoretical model a low-frequency limit was considered where eigenmodes are weakly damped, thus they were approximated by normal acoustic modes for rigid room walls. The effect of acoustic coupling on the mode frequency, the integrated density of states (IDOS) and the existence surface of modes were investigated for several coupling areas. Numerical results indicate that a decrease in coupling area causes a decrease of IDOS and results in a stronger localization of modes.

Keywords:

coupled rooms, spectral characteristics, localization of modes

Affiliations:
Meissner M.-IPPT PAN
18.Janczur R., Walerian E.M., Meissner M., Czechowicz M., Application of simulation program to specific urban situation, APPLIED ACOUSTICS, ISSN: 0003-682X, DOI: 10.1016/j.apacoust.2008.11.002, Vol.70, No.7, pp.973-985, 2009
Abstract:

In the paper, the simulation program predicting the sound level has been applied to one of buildings neighbouring a road. In the simulation are considered: geometry of road surroundings, the shape of the investigated building façade including, road geometry (number of lanes and their positions) and traffic structure (vehicle flow rates and their average speeds). Adjustable accuracy in an urban system modelling allows finding the model which is adequate to the real system. For the model of the accuracy limited by the simulation error due to vehicle speed estimation, by comparison with the field measurement, the model validation range has been established. Based on the simulation adjustable accuracy, possibilities of the validation range extension have been analysed.

Keywords:

simulation, traffic noise, noise protecting means

Affiliations:
Janczur R.-IPPT PAN
Walerian E.M.-IPPT PAN
Meissner M.-IPPT PAN
Czechowicz M.-IPPT PAN
19.Meissner M., Computer modelling of coupled spaces: variations of eigenmodes frequency due to a change in coupling area, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.34, No.2, pp.157-168, 2009
Abstract:

Acoustically coupled spaces have recently been drawing more and more attention in the architectural acoustics community, thus a determination of shapes and frequencies of eigenmodes in these room systems from computer-based models has become increasingly significant. In this investigation, an eigenvalue problem was solved numerically for a simple room system consisting of two connected rectangular spaces. In a numerical procedure, the forced oscillator method with a finite difference algorithm was applied. In order to determine the influence of irregularity of system shape on eigenmodes frequency, a modal behaviour in the coupled spaces was studied for several sizes of coupling area. Calculation results have shown that with the exception of a fundamental mode, the changes in resonant frequencies were relatively small. However, an increase in a system irregularity led to a coincidence of frequencies of neighbouring modes and variations in a sequence of modes on a frequency axis, which both contributed to a degeneration of eigenmodes.

Keywords:

coupled spaces, modal analysis, degenerate modes, mode localization

Affiliations:
Meissner M.-IPPT PAN
20.Meissner M., Application of Hilbert transform-based methodology to computer modelling of reverberant sound decay in irregularly shaped rooms, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.34, No.4, pp.491-506, 2009
Abstract:

A study into the application of the Hilbert transform in numerical simulations of reverberant sound decay in irregularly shaped enclosures is presented. It is shown that there are some limitations in the use of this integral transform to exponentially decaying harmonic signals because the integration result consists not only of a signal, which differs from the original one by a phase shift of pi/2, but also of a decaying nonoscillating signal occurring due to the fact that a spectrum of exponential function is unbounded. An initial amplitude of this signal is directly proportional to the ratio between a damping coefficient and a mode frequency, thus for lightly damped rooms, where this ratio is much smaller than unity, it can be neglected. Results of numerical simulation carried out for L-shaped enclosure indicate that the Hilbert transform is a useful tool in calculating instantaneous properties of reverberant sound, especially an envelope of the sound pressure level. It is of special importance in the case of irregularly shaped rooms, where a deviation from the exponential sound decay often occurs because of differences between reverberant responses for particular modes.

Keywords:

Hilbert transform, analytic signal, irregularly shaped enclosures, reverberant room response, reverberation time, early and late decay times

Affiliations:
Meissner M.-IPPT PAN
21.Meissner M., Influence of wall absorption on low-frequency dependence of reverberation time in room of irregular shape, APPLIED ACOUSTICS, ISSN: 0003-682X, DOI: 10.1016/j.apacoust.2007.02.004, Vol.69, No.7, pp.583-590, 2008
Abstract:

In this paper, a modal analysis was used to describe a reverberation phenomenon in a room of complex shape. A theoretical model was limited to low sound frequencies, when eigenmodes are lightly damped, thus they may be approximated by uncoupled normal acoustic modes of a hard-walled room. A utility of this method was demonstrated in a numerical example where the enclosure in a form of two coupled rooms was considered. A reverberation time was evaluated from a time decay of spatial root mean square pressure, the overall measure of room pressure. The results of calculations, performed for three different distributions of absorbing materials on room walls, showed how various location of the material can effect a dependence of the reverberation time on a frequency of sound source.

Keywords:

coupled enclosures, modal analysis, reverberation time

Affiliations:
Meissner M.-IPPT PAN
22.Meissner M., Influence of absorbing material distribution on double slope sound decay in L-shaped room, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.33, No.4S, pp.159-164, 2008
Abstract:

The sound decay process in L-shaped room was the subject of this investigation. The room with walls covered by the low absorbent material constituted the initial configuration for the study. To decrease a reverberation time, alterations of acoustic room properties were carried out by adding a high absorbent material on lateral room walls. Two different material configurations were considered and their effects on a double slope sound decay were analysed. In order to predict the behaviour of decay curve, a numerical implementation based on the wave theory was applied. A space distribution of eigenfunctions was computed using the forced oscillator method with a finite difference algorithm. Numerical results have demonstrated that an introduction of high absorbent material on selected room walls may cause an intense double slope effect. It is characterized by rapid initial and slow late decays, thus the decay curve exhibits so-called a “sagging” appearance. It was found also that a phenomenon of mode localization is an important factor in modifying the double slope sound decay.

Keywords:

coupled rooms, modal analysis, reverberation, double slope effect, localization of eigenmodes

Affiliations:
Meissner M.-IPPT PAN
23.Meissner M., Computational studies of steady-state sound field and reverberant sound decay in a system of two coupled rooms, CENTRAL EUROPEAN JOURNAL OF PHYSICS, ISSN: 1895-1082, DOI: 10.2478/s11534-007-0016-7, Vol.5, No.3, pp.293-312, 2007
Abstract:

The acoustical properties of an irregularly shaped room consisting of two connected rectangular subrooms were studied. An eigenmode method supported by a numerical implementation has been used to predict acoustic characteristics of the coupled system, such as the distribution of the sound pressure in steady-state and the reverberation time. In the theoretical model a low-frequency limit was considered. In this case the eigenmodes are lightly damped, thus they were approximated by normal acoustic modes of a hard-walled room. The eigenfunctions and eigenfrequencies were computed numerically via application of a forced oscillator method with a finite difference algorithm. The influence of coupling between subrooms on acoustic parameters of the enclosure was demonstrated in numerical simulations where different distributions of absorbing materials on the walls of the subrooms and various positions of the sound source were assumed. Calculation results have shown that for large differences in the absorption coefficient in the subrooms the effect of modal localization contributes to peaks of RMS pressure in steady-state and a large increase in the reverberation time.

Keywords:

coupled rooms, modal analysis, reverberation time, modes localization

Affiliations:
Meissner M.-IPPT PAN
24.Meissner M., Analysis of non-exponential sound decay in an enclosure composed of two connected rectangular subrooms, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.32, No.4S, pp.213-220, 2007
Abstract:

Acoustically coupled rooms have recently been drawing more and more attention in the architectural acoustics community. Determination of decay times in these coupled rooms from computer-based models has become increasingly significant. In computational modelling of coupled enclosures the geometrical acoustics methods do not apply at lower frequencies, and models must account for the wave-nature of sound fields, especially modal effects. In this investigation a combination of modal analysis with finite-difference algorithm was used to predict a decay in the sound field energy in an enclosure composed of two connected rectangular subrooms. Random incidence absorption coefficients inside subrooms have been modified in this study to create different configurations of absorbing materials on subrooms walls. When one of these subrooms was much more absorbent than the other one, calculation results have shown that, at any frequencies, there existed both the initial sudden and the late slow decrease in the sound field energy. This effect was characterized by two metrics: early decay time (EDT) and late decay time (LDT) determined from a sound level decay from –50 to –60 dB. The analysis of numerical data confirmed that the most influential factor in realizing the non-exponential sound decay is a phenomenon of eigenmodes localization.

Keywords:

coupled rooms, reverberation, double-sloped sound decay, localization of modes

Affiliations:
Meissner M.-IPPT PAN
25.Janczur R., Walerian E.M., Meissner M., Czechowicz M., Influence of vehicle noise emission directivity on sound level distribution in a canyon street. Part II: Experimental verification, APPLIED ACOUSTICS, ISSN: 0003-682X, DOI: 10.1016/j.apacoust.2005.12.003, Vol.67, pp.659-679, 2006
Abstract:

In the paper, predictions of relative sound level distribution on building facades in city-centres obtained by using the simulation PROP11 program are compared with measurements. The simulation involves the geometry of surrounding buildings, road geometry (number of lanes and their positions) and traffic structure (vehicle flow rates and their average speeds). The agreement between measurement and simulation results is tested for different directivity characteristics of an equivalent point source representing the vehicles.

Keywords:

predicted sound level in built-up area, vehicle noise emission directivity

Affiliations:
Janczur R.-IPPT PAN
Walerian E.M.-IPPT PAN
Meissner M.-IPPT PAN
Czechowicz M.-IPPT PAN
26.Meissner M., The effect of modal localization on reverberant energy decay in a case of two acoustically coupled rooms, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.31, pp.239-245, 2006
Abstract:

In the paper a modal analysis was used to describe a reverberation phenomenon in an irregularly shaped room. A theoretical model was limited to low sound frequencies, when eigenmodes are lightly damped, thus they may be approximated by normal acoustic modes of a hard-walled room. A utility of this method was demonstrated in a numerical example where the room in a form of two acoustically coupled rectangular subrooms was considered. A reverberation time was evaluated individually for each subroom from time decay of acoustic pressure amplitude for different distributions of absorbing materials of room walls and various positions of sound source under the condition that a total room absorption remained constant. Calculation results have shown a great influence of modes localization on a reverberant energy decay for a large difference between the absorption coefficients of walls in subrooms, because in this case for frequencies of some localized modes a substantial increase in the reverberation time was observed.

Keywords:

room acoustics, modal analysis, reverberation time, modes localization

Affiliations:
Meissner M.-IPPT PAN
27.Meissner M., The response of Helmholtz resonator to external excitation. Part II: flow-induced resonance, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.30, No.1, pp.57-71, 2005
Abstract:

In the paper a phenomenon of sound production in a resonator driven by an air jet has been investigated. Measurements of sound spectra at the closed end of the resonator cavity were performed to determine the influence of the jet velocity on the frequency and amplitude of excited acoustic oscillations. It was found that in the sound generation process two ranges of the jet velocity could be distinguished where different variations of the oscillation frequency with the growing jet velocity were observed. After the onset of oscillation the frequency increased fast with growing jet velocity and the frequency increment was directly proportional to a value of jet velocity. At higher flow velocities an increase in the frequency was still observed, but the frequency growth was much smaller. The experiment has shown also that due to an excitation of mechanical vibrations of the resonator elements a rapid change in the oscillation frequency occurred. Finally, the experimental data were compared to calculation results to examine the accuracy of the theoretical model, in which a force driving the resonator was predicted from the vortex sound theory and the resonator was modelled by an equivalent impedance circuit.

Keywords:

sound generation, flow-induced resonance, acoustic resonators

Affiliations:
Meissner M.-IPPT PAN
28.Meissner M., Influence of room geometry on low-frequency modal density, spatial distribution of modes and their damping, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.30, pp.205-210, 2005
Abstract:

Acoustical properties of two rooms of irregular shapes have been investigated theoretically by a system of eigenmodes, which for low frequencies and weak losses on walls can be well approximated by a system of normal acoustic modes of hard wall room. The eigenfunctions and eigenfrequencies were determined numerically with an application of the forced oscillator method with a finite difference algorithm. It was found that a geometrical irregularity has three main effects. First, the low-frequency modal density is changed. Second, some of eigenmodes are localized, thus for particular frequencies a vibration amplitude will be enhanced locally inside the room. Third, the acoustic energy losses inside the room are increased with the amplitude of vibration on walls.

Keywords:

room acoustics, modal analysis, eigenfunctions, modal density, modes localization

Affiliations:
Meissner M.-IPPT PAN
29.Meissner M., The response of Helmholtz resonator to external excitation. Part I: acoustically induced resonance, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.29, No.1, pp.107-121, 2004
Abstract:

The first of two companion papers theoretical and experimental results are presented for a Helmholtz resonator subject to external excitation by an acoustic plane wave. The response of the resonator was analysed in terms of the relation between the pressure induced in the interior of the resonator and the driving pressure. Equations for the resonance frequency and the quality factor were developed for the cavity that was a rectangular parallelepiped with a centered circular orifice. The flow from the cavity had a constant velocity profile. The resonator was modelled by an equivalent impedance circuit, predicted from the classic theory of sound radiation, with an additional resistive term connected with the viscous action inside the orifice. The theoretical results were compared with experimental data for a frequency chosen so as to tune the system to the lowest resonance mode. The experiment has shown that the acoustic response of resonator was changed considerably when mechanical vibrations of the resonator elements were excited. A phenomenon of flow-induced resonance in the considered system geometry will be presented in the companion paper.

Keywords:

Helmholtz resonator, flow-induced resonanse, acoustic response of resonator

Affiliations:
Meissner M.-IPPT PAN
30.Meissner M., Excitation of Helmholtz resonator by grazing air flow, JOURNAL OF SOUND AND VIBRATION, ISSN: 0022-460X, DOI: 10.1006/jsvi.2001.4219, Vol.256, No.2, pp.382-388, 2002
Keywords:

cavity resonator, flow-excited sound, Strouhal number

Affiliations:
Meissner M.-IPPT PAN
31.Meissner M., Aerodynamically excited acoustic oscillations in cavity resonator exposed to an air jet, ACTA ACUSTICA UNITED WITH ACUSTICA, ISSN: 1610-1928, Vol.88, No.2, pp.170-180, 2002
Abstract:

Experimental and theoretical results are presented for a cavity resonator driven by an air jet. Cavity sound spectra have been investigated to found a dependence of sound frequency and amplitude versus jet speed. Two ranges of the jet speed were distinguished. In the stage I, identified with low speed range, the frequency increased fast with jet speed and a frequency increment was proportional to jet speed as in the edge–tones phenomenon. In a stage II, corresponding to higher jet speeds, an increase in the frequency was still observed, but a frequency growth was much smaller. A correlation of experimental data has shown that the observed oscillation amplitudes are within moderate–range. A theoretical model based on moving compact vortices was presented to describe flow–acoustic interaction in a resonator opening and find an aerodynamic force driving a resonator. A response of resonator was modelled by equivalent impedance circuit with added nonlinear term. From final equations a frequency and an amplitude of oscillation were calculated. A support for the proposed theory is provided by favourable comparison between theoretical predictions and experimental data.

Keywords:

cavity resonator, air jet, sound generation, vortex street

Affiliations:
Meissner M.-IPPT PAN
32.Meissner M., Acoustic modes induced by flow in a pipe with two closed side-branches, APPLIED ACOUSTICS, ISSN: 0003-682X, Vol.63, No.10, pp.1071-1083, 2002
Abstract:

An air flow in a pipe with two closed side-branches can induce high pressure pulsations in a pipe system. This phenomenon has been investigated and the results are reported in this paper. A simple theoretical model based on a wave transmission was used to determine a resonance condition associated with an acoustic coupling between branches. In the model a plane wave approximation and an impedance representation of a branch were applied. The experiment was carried out in a pipe system with a relatively large distance between branches compared to branch lengths. A frequency and a pressure of pulsations were measured in a wide range of length of downstream branch. A support for the theory is provided by a favorable comparison between experimental data and calculated resonant frequencies of the system.

Keywords:

pipe system, closed side-branches, acoustic resonance

Affiliations:
Meissner M.-IPPT PAN
33.Meissner M., Absorption properties of Helmholtz resonator at high amplitude incident sound, ACTA ACUSTICA UNITED WITH ACUSTICA, ISSN: 1610-1928, Vol.86, No.6, pp.985-991, 2000
Abstract:

The sound attenuation in a Helmholtz resonator subjected to a plane incident wave is examined. The resonator closing a tube is considered. The average acoustic power absorbed by vortical field has been calculated in the low frequency range with the aid of the appropriate conservation equations. Considering this power loss and losses due to viscous damping inside the resonator orifice, the change of absorption properties of the resonator is analyzed. Results of this study indicate that the peak of the absorption coefficient occurs when the loss resistance is equal to the radiation resistance. Plots of the theoretically predicted absorption coefficient and normalized loss resistance as a function of incident pressure amplitude are in good agreement with experimental data obtained for different orifice diameters.

Keywords:

Helmholtz resonator, sound absorption, nonlinear resistance

Affiliations:
Meissner M.-IPPT PAN
34.Meissner M., The influence of acoustic nonlinearity on absorption properties of Helmholtz resonators. Part II: experiment, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.25, No.2, pp.175-190, 2000
Abstract:

An experimental study of an effect of the acoustic nonlinearity on absorption properties of Helmholtz resonators is presented in this work. By use of the classical standing wave method the changes in the absorption coefficient and the resonators impedance were investigated at moderate and high amplitudes of incident wave. As a result of nonlinearity a high absorption at resonance frequencies was observed and then a decrease in this absorption with increasing amplitude. Measurements of the total loss resistance of resonators have indicated that a change in the resistance at high amplitudes depends strongly on resonator orifice area, the smaller area - the higher increase in the resistance. The experimental results have also shown a growth in resonators reactance which causes an increase in resonance frequency. Quite a good agreement between experimental data and the theory presented in Part I was found.

Keywords:

Helmholtz resonator, acoustic nonlinearity, absorption coefficient

Affiliations:
Meissner M.-IPPT PAN
35.Meissner M., The influence of acoustic nonlinearity on absorption properties of Helmholtz resonators. Part I: theory, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.24, No.2, pp.179-190, 1999
Abstract:

This is the first of two companion papers concerned with the nonlinear absorption of Helmholtz resonators at a high amplitude incident wave. The phenomenon has been examined theoretically by use of a model of the acoustic field in the neighborhood of the resonator placed at the end of cylindrical tube. The calculation results have shown that the peak of the absorption coeficient occurs when the nonlinear resistance is equal to the radiation resistance of the resonator. The full experimental investigations of this phenomenon and a comparison between theoretical and experimental data will be presented in the companion paper (Part II).

Keywords:

Helmholtz resonator, nonlinear sound absorption, high amplitude incident sound

Affiliations:
Meissner M.-IPPT PAN
36.Meissner M., Badania odpowiedzi układów rezonansowych na pobudzenie akustyczne i aerodunamiczne (Praca habilitacyjna), Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.8, pp.1-233, 1998
37.Meissner M., Flow–excited acoustic pulsations in ducts with closed side branches, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.22, No.2, pp.153-167, 1997
Abstract:

In flow ducts with closed side branches strong acoustic pulsations are often induced. This was shown by test results performed for systems with a single side branch and co-axial branches with the same lengths. With growing the flow velocity an excitation of successive resonant modes was observed. Their frequencies were increased together with the flow velocity but at peaks of sound pressure there was an excellent agreement between measurements results and theoretical predictions. A conversion of fluctuating flow energy to energy of resonant acoustic field was included in theoretical consideration by means of negative resistance in impedance model of branches. Hence, it was possible to predict a stronger nonlinearity in the case of a duct with co-axial branches. It was found that a characteristic parameter of the analyzed phenomenon is Strouhal number. Its values for all modes are within the same range approximately and, in addition, it determines a change of acoustic inertance at the branch opening.

Keywords:

closed side branches, Strouhal number, resonant modes

Affiliations:
Meissner M.-IPPT PAN
38.Meissner M., Czechowicz M., Experimental investigation of flow-induced acoustic oscillations in piping system with closed branches, APPLIED ACOUSTICS, ISSN: 0003-682X, Vol.45, No.4, pp.359-375, 1995
Abstract:

An experimental study of flow-excited acoustic oscillations in piping systems with closed branches is presented in this paper. An influence of acoustic interactions between branches on a generated sound was investigated in arrangements with two and three branches. Significant changes of frequency and level of oscillation in terms of branch lengths were observed. In the system with three branches, at the specified lengths of one branch, a cancellation of oscillations was noticed.

Keywords:

piping system, closed side branches, flow-induced oscillations

Affiliations:
Meissner M.-IPPT PAN
Czechowicz M.-IPPT PAN
39.Meissner M., Oscylacje samowzbudne w rurociągu z zamkniętymi odgałęzieniami, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.18, pp.1-40, 1994
40.Meissner M., Zjawisko nieliniowości przy oddziaływaniu ciśnienia akustycznego na rezonator Helmholtza, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.19, pp.1-50, 1994
41.Meissner M., Ranachowski Z., Modelling of acoustic emission sources, ACTA ACUSTICA UNITED WITH ACUSTICA, ISSN: 1610-1928, Vol.79, No.2, pp.186-189, 1993
Keywords:

acoustic emission, plate vibrations, frequency spectrum

Affiliations:
Meissner M.-IPPT PAN
Ranachowski Z.-IPPT PAN
42.Meissner M., Discrete sound induced by low Mach number flow over side branch deep cavity in a rectangular duct, ARCHIVES OF ACOUSTICS, ISSN: 0137-5075, Vol.17, No.2, pp.287-305, 1992
Abstract:

This paper presents the model of the discrete sound induction effect due to a flow over deep cavity in the wall of a rectangular duct. Theoretical analysis applies shear layer approximation with a vortex sheet, with deflection satisfying the Kutta-Żukowski condition, and an equivalent impedance system of a deep cavity with cavity impedance change in the presence of the flow included. The applied theoreticl method makes it possible to determine the effect of resonanse modes of the cavity on disturbances of the vortex sheet and also to determine the frequency and relative value of pressure amplitude in the case of a discrete sound.

Keywords:

discrete sound generation, vortex sheet, deep cavity

Affiliations:
Meissner M.-IPPT PAN
43.Meissner M., Ranachowski Z., Generacja i propagacja wzorcowych impulsów emisji akustycznej, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.36, pp.1-47, 1992
44.Meissner M., Generacja dźwięku o dyskretnej częstotliwości przy opływie wnęki głębokiej przez strumień gazu (Praca doktorska), Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.8, pp.1-144, 1991
45.Meissner M., Self-sustained deep cavity oscillations induced by grazing flow, ACTA ACUSTICA UNITED WITH ACUSTICA, ISSN: 1610-1928, Vol.62, No.3, pp.220-228, 1987
Abstract:

This paper is concerned with a model of sound generation in a case of the deep cavity exposed to a grazing mean air flow. The problem was analyzed theoretically by means of infinitely thin shear layer assumption and the description of acoustic response of the cavity. The response was determined with the aid of the impedance model of flow excited quarter-wave resonator, including the nonlinear orifice damping. The parameters of unstable motion in the slot were found, basing on continuity conditions across the orifice plane. Calculated values were used in order to determine the acoustic pressure in far-field area. The theoretical predictions were compared to experimental results.

Keywords:

deep cavity, discrete sound generation, grazing flow

Affiliations:
Meissner M.-IPPT PAN

List of chapters in recent monographs
1.
498
Meissner M., Postępy Akustyki 2016, rozdział: Improving acoustics of hard-walled rectangular room by ceiling treatment with absorbing material, Polskie Towarzystwo Akustyczne, Oddział Warszawski, Warszawa, Poland, pp.413-424, 2016
2.
499
Meissner M., Postępy Akustyki 2016, rozdział: Wave-based method for simulating small room acoustics, Polskie Towarzystwo Akustyczne, Oddział Warszawski, Warszawa, Poland, pp.425-436, 2016
3.
408
Meissner M., Progress of Acoustics, rozdział: Numerical Analysis of Sound Decay Process in Acoustically Coupled Spaces, Polskie Towarzystwo Akustyczne, pp.497-508, 2015
4.
190
Meissner M., Renewable energy: innovative technologies and new ideas, rozdział: Acoustics of irregular rooms in buildings: low-frequency mathematical modelling and numerical simulation, Warsaw University of Technology (Warsaw), Chwieduk D., Domański R., Jaworski M. (Eds.), pp.265-272, 2008
Editor of monographs
1.
500
Meissner M., Postępy Akustyki 2016, Polskie Towarzystwo Akustyczne, Oddział Warszawski, Warszawa, Poland, pp.1-682, 2016

Conference papers
1.Meissner M., Metoda zwiększająca dokładność dyskretnej transformaty Hilberta przy wyznaczaniu amplitudy i częstotliwości sygnałów wibroakustycznych, WibroTech 2017, XIX Konferencja Naukowa Wibroakustyki i Wibrotechniki XIV Ogólnopolskie Seminarium Wibroakustyka w Systemach Technicznych, 2017-05-19/05-20, Pruszków (PL), pp.71-74, 2017
Keywords:

wibroakustyka, analiza sygnałów, dyskretna transformata Hilberta

Affiliations:
Meissner M.-IPPT PAN
2.Meissner M., Computer simulation of active intensity vector field in enclosure of irregular geometry, 59th Open Seminar on Acoustics, 2012-09-10/09-14, Boszkowo (PL), pp.163-166, 2012
Abstract:

The modal expansion method has been used to formulate expressions for real and imaginary parts of the complex sound intensity inside enclosures. Based on theoretical results, the computer program has been developed to simulate the active intensity vector field inside L-shaped enclosure. Calculation results have shown that a distribution of the active intensity is strongly influenced by the modal localization and the typical objects in the active intensity field are energy vortices and saddle points positioned irregularly inside the room. It was found that an increase in a sound attenuation results in the change of vortex positions and can cause the formation of new vortices. An influence of the wall impedance on the quantitative relation between the active and reactive intensities was also studied and it was concluded that for very small sound damping the behavior of the sound intensity is basically only oscillatory.

Keywords:

room acoustics, active intensity vector field

Affiliations:
Meissner M.-IPPT PAN
3.Meissner M., The influence of source location on the distribution of steady-state sound field inside two coupled rooms, 58th Open Seminar on Acoustics joined with 2nd Polish-German Structured Conference on Acoustics, 2011-09-13/09-16, Jurata (PL), Vol.2, pp.57-66, 2011
Abstract:

In the paper, the computer modelling application based on the modal expansion method is developed to study an influence of a sound source location on a steady-state response of coupled rooms. In the research, an eigenvalue problem is solved numerically for a room system consisting of two rectangular spaces connected to one another. A numerical procedure enables the computation of shape and frequency of eigenmodes, and allows one to predict the potential and kinetic energy densities in a steady-state. In the first stage, a frequency room response for several source positions is investigated, demonstrating large deformations of this response for strong and weak modal excitations. Next, particular attention is given to studying how the changes in a source position influence the room response when a source frequency is tuned to a resonant frequency of a strongly localized mode.

Affiliations:
Meissner M.-IPPT PAN
4.Meissner M., Influence of absorbing material distribution on double slope sound decay in L-shaped room, 55th Open Seminar on Acoustics, 2008-09-08/09-12, Piechowice (PL), pp.493-498, 2008
5.Meissner M., Zależność od częstotliwości rozkładu ciśnienia akustycznego w układzie dwóch połączonych ze sobą pomieszczeń prostopadłościennych, 53th Open Seminar on Acoustics, 2006-09-11/09-15, Zakopane (PL), pp.237-242, 2006
Abstract:

Modelowanie pola dźwiękowego w pomieszczeniach sprzężonych akustycznie stanowiło przedmiot wielu prac badawczych, ponieważ przykładami tego rodzaju obiektów są teatry, gdzie szereg loż połączonych jest z salą główną, oraz kościoły, w których występuje wiele naw oraz kaplic. W pracy, przy zastosowaniu analizy modalnej i implementacji numerycznej przeanalizowano dla małych częstotliwości rozkład ciśnienia akustycznego w stanie ustalonym dla sali złożonej z dwóch połączonych ze sobą pomieszczeń prostopadłościennych. Wyniki symulacji numerycznej uzyskane dla różnego usytuowania materiału pochłaniającego wykazały silną zależność rozkładu ciśnienia od częstotliwości dźwięku. Zaobserwowano to szczególnie dla dużych różnic we własnościach absorpcyjnych obu pomieszczeń, gdyż w tych przypadkach dla szeregu częstotliwości pojawiły się silne maksima ciśnienia związane z efektem lokalizacji modów własnych.

Affiliations:
Meissner M.-IPPT PAN

Patents
Numer/data zgłoszenia patentowego
Ogłoszenie o zgłoszeniu patentowym
Twórca / twórcy
Tytuł
Kraj i Nazwa uprawnionego z patentu
Numer patentu
Ogłoszenie o udzieleniu patentu
pdf
396560
2011-10-06
BUP 08/13
2013-04-15
Raunmiagi Z., Ranachowski Z., Meissner M.
Sposób i urządzenie do oceny stanu technicznego rozpylacza paliwa, do silnika z samoczynnym zapłonem
PL, Akademia Morska w Szczecinie
217570
WUP 07/14
2014-07-31