Analysis of the Room Acoustic with Impedance Boundary Conditions in the Full Range of Acoustic Frequencies

• Autorzy: Prędka Edyta , Brański Adam

Identyfikatory

DOI

10.24425/aoa.2020.132484

• Języki publikacji: EN

Abstrakty

EN

An efficiency of the nonsingular meshless method (MLM) was analyzed in an acoustic indoor problem. The solution was assumed in the form of the series of radial bases functions (RBFs). Three representative kinds of RBF were chosen: the Hardy’s multiquadratic, inverse multiquadratic, Duchon’s functions. The room acoustic field with uniform, impedance walls was considered. To achieve the goal, relationships among physical parameters of the problem and parameters of the approximate solution were first found. Physical parameters constitute the sound absorption coefficient of the boundary and the frequency of acoustic vibrations. In turn, parameters of the solution are the kind of RBFs, the number of elements in the series of the solution and the number and distribution of influence points. Next, it was shown that the approximate acoustic field can be calculated using MLM with a priori error assumed. All approximate results, averaged over representative rectangular section of the room, were calculated and then compared to the corresponding accurate results. This way, it was proved that the MLM, based on RBFs, is efficient method in description of acoustic boundary problems with impedance boundary conditions and in all acoustic frequencies.

Słowa kluczowe

EN

architectural acoustics; meshless method; radial bases functions; impedance boundary condition

• Wydawca: Instytut Podstawowych Problemów Techniki PAN ; Komitet Akustyki PAN ; Polskie Towarzystwo Akustyczne
• Czasopismo: Archives of Acoustics
• Rocznik: 2020
• Tom: Vol. 45, No. 1
• Strony: 85--92
• Opis fizyczny: Bibliogr. 38 poz., rys., wykr.

Twórcy

autor

Prędka Edyta

• Department of Complex Systems, Faculty of Electrical and Computer Engineering Technical University of Rzeszów, al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland

autor

Brański Adam

• Department of Complex Systems, Faculty of Electrical and Computer Engineering Technical University of Rzeszów, al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland

Bibliografia

• 1. Antunesp R. S., Valtchev S. S. (2010), A meshfree numerical method for acoustic wave propagation problems in planar domains with corners and cracks, Journal of Computational and Applied Mathematics, 234 (9): 2646-266, doi: 10.1016/j.cam.2010.01.031.
• 2. Aretz M., Dietrich P., Vorländer M. (2014), Application of the mirror source method for low frequency sound prediction in rectangular rooms, Acta Acustica united with Acustica, 100 (2): 306-319, doi: 10.3813/AAA.918710.
• 3. Atluri S. N. (2004), The meshless method (MLPG) for domain & BIE discretization, Tech Science Press, Forsyth, GA, USA.
• 4. Bajko J., Niedoba P., Cermak L., Cham J. I. (2017), Simulation of the acoustic wave propagation using a meshless method, EPJ Web of Conferences 143, 02003, EFM 2016, doi: 10.1051/epjconf/201714302003.
• 5. Borkowski M. (2015), 2D capacitance extraction with direct boundary methods, Engineering Analysis with Boundary Elements, 58: 195-201, doi: 10.1016/j.enganabound.2015.04.017.
• 6. Boucher M., Pluymers B., Desmet W. (2016), Interference effects in phased beam tracing using exact half-space solutions, The Journal of the Acoustical Society of America, 140 (6): 4204-4212, doi: 10.1121/1.4971283.
• 7. Brański A., Borkowska D. (2015a), Effectiveness of nonsingular solution of the boundary problems based on Trefftz methods, Engineering Analysis with Boundary Elements, 59: 97-104, doi: 10.1016/j.enganabound.2015.04.016.
• 8. Brański A., Borkowska D. (2015b), Galerkin versions of nonsingular Trefftz methods derived from variational formulations for 2D Laplace problem, Acta Physica Polonica A, 128 (1A): A50-A55, doi: 10.12693/APhysPolA.128.A-50.
• 9. Brański A., Borkowski M., Borkowska D. (2012), A comparison of boundary methods based on inverse variational formulation, Engineering Analysis with Boundary Elements, 36 (4): 505-510, doi: 10.1016/j.enganabound.2011.11.004.
• 10. Brański A., Kocan-Krawczyk A., Prędka E. (2017), An influence of the wall acoustic impedance on the room acoustics. The exact solution, Archives of Acoustics, 42 (4): 677-687, doi: 10.1515/aoa-2017-0070.
• 11. Brański A., Prędka E. (2017), Effectiveness of the inverse multi-quadratic RBF in acoustic indoor problem, Open Seminar on Acoustics, Gliwice, 55-58.
• 12. Brański A., Prędka E. (2018), Nonsingular meshless method in an acoustic indoor problem, Archives of Acoustics, 43 (1): 75-82, doi: 10.24425/118082.
• 13. Chen W., Fu Z., Zhang C. Z. (2013), Recent advances on radial function collocation methods, Springer, Berlin.
• 14. Cheng A. H.-D. (2000), Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions, Engineering Analysis with Boundary Elements, 24 (7-8): 531-538, doi: 10.1016/S0955-7997(00)00033-3.
• 15. Dobrucki A., Zółtogórski B., Pruchnicki P., Bolejko R. (2010), Sound-absorbing and insulating enclosures for ultrasonic range, Archives of Acoustics, 35 (2): 157-164.
• 16. Duchon J. (1976), Splines minimizing rotation invariant semi-norms in Sobolev spaces, Lecture notes in mathematics, Vol. 571, pp. 85-110, Springer, New York.
• 17. Fish J., Belytschko T. (2007), A first course in finite element elements, John Wiley & Sons.
• 18. Fu Z.-J., Chen W., Chen J.-T., Qu W.-Z. (2014), Singular boundary method: three regularization approaches and exterior wave applications, CMES: Computer Modeling in Engineering & Sciences, 99 (5): 417-443, doi: 10.3970/cmes.2014.099.417.
• 19. Hardy R. L. (1971), Multiquadric equations of topography and other irregular surfaces, Journal of Geophysical Research, 76 (8): 1905-1915, doi: 10.1029/JB076i008p01905.
• 20. Kamisiński T. (2012), Correction of acoustics in historic opera theatres with the use of Schroeder diffuser, Archives of Acoustics, 37 (3): 349-354.
• 21. Kamisiński T., Kulowski A., Kinasz R. (2016), Can historic interiors with large cubature be turned acoustically correct?, Archives of Acoustics, 41 (1): 3-14, doi: 10.1515/aoa-2016-0001.
• 22. Kuttruff H. (2000), Fundamentals of physical acoustics. Room acoustic, Wiley-Interscience, New York.
• 23. Majkut L., Olszewski R. (2014), Acoustic eigenanalysis with radial basis functions, Acta Physica Polonica A, 125 (4A): 77-82, doi: 10.12693/APhys-PolA.125.A-7.
• 24. Meissner M. (2009), Computer modelling of coupled spaces: variations of eigenmodes frequency due to a change in coupling area, Archives of Acoustics, 34 (2): 157-168.
• 25. Meissner M. (2013), Evaluation of decay times from noisy room responses with puretone excitation, Archives of Acoustics, 38 (1): 47-54.
• 26. Meissner M. (2016a), Improving acoustics of hard-walled rectangular room by ceiling treatment with absorbing material, Progress of Acoustics, Polish Acoustical Society, Warsaw Division, Warszawa-Białowieża, pp. 413-423.
• 27. Meissner M. (2016b), Wave-based method for simulating small room acoustics, Progress of Acoustics, Polish Acoustical Society, Warsaw Division, Warszawa-Białowieża, pp. 425-436.
• 28. Piechowicz J., Czajka I. (2012), Estimation of acoustic impedance for surfaces delimiting the volume of an enclosed space, Archives of Acoustics, 37 (1): 97-102.
• 29. Pilch A., Kamisiński T. (2011), The effect of geometrical and material modification of sound diffusers on their acoustic parameters, Archives of Acoustics, 36 (4): 955-966.
• 30. Prędka E. (2016), Nonsingular MLM via the multiquadratic RBF in an acoustic indoor problem, Open Seminar on Acoustics, Warszawa-Białowieża, pp. 437-440.
• 31. Rindel J. H. (2010), Room acoustic prediction modeling, XXIII Encontro Da Socieda de Brasileira Deacústica, Salvador-Ba,18 A21 De Maio De.
• 32. Rubacha J., Pilch A., Zastawnik M. (2012), Measurements of the sound absorption coefficient of audytorium seats for various geometries of the samples, Archives of Acoustics, 37 (4): 483-488.
• 33. Shojaei A. (2016), A meshless method for unbounded acoustic problems, The Journal of the Acoustical Society of America, 139 (5): 2613-2623, doi: 10.1121/1.4948575.
• 34. Shojaei A., Galvanetto U., Rabczuk T., Jenabi A., Zaccariotto M. (2019), A generalized finite difference method based on the Peridynamic differential operator for the solution of problems in bounded and unbounded domains, Computer Methods in Applied Mechanics and Engineering, 343: 100-126, doi: 10.1016/j.cma.2018.08.033.
• 35. Shojaei A., Mossaiby F., Zaccariotto M., Galvanetto U. (2019), A local collocation method to construct Dirichlet-type absorbing boundary conditions for transient scalar wave propagation problems, Computer Methods in Applied Mechanics and Engineering, 356, 629-651, doi: 10.1016/j.cma.2019.07.033.
• 36. Siltanen S., Lokki T., Savioja L. (2010), Rays or waves? Understanding the strengths and weaknesses of computational room acoustics modeling techniques, Proceedings of the International Symposium on Room Acoustics, ISRA, 29-31 August 2010, Melbourne, Australia.
• 37. Sladek V., Sladek J., Tanaka M. (2000), Optimal transformations of the integration variables in computation of singular integrals in BEM, Journal for Numerical Method in Engineering, 47 (7): 1263-1283, doi: 10.1002/(SICI)1097-0207(20000310)47:7<1263::AIDNME811>3.0.CO;2-I.
• 38. Suh J., Nelson P. (1999), Measurement of transient response of rooms and comparison with geometrical acoustic models, The Journal of the Acoustical Society of America, 105 (4): 2304-2317, doi: 10.1121/1.426837.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).