Numerical solutions of the acoustic eigenvalue equation in the rectangular room with arbitrary (uniform) wall impedances

Bistafa, Sylvio R.; Morrissey, John W.

doi:10.1016/s0022-460x(02)01123-9

Cited by 29 publications

(21 citation statements)

References 3 publications

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“…In mathematical interpretation, the F (x) constitutes the solution of the radial part of the Bessel's differential equation in spherical coordinates (Korn, Korn, 1968;McLachlan, 1964;Evans, 2002). Here, the 0-order, spherical Hankel function of the second kind h (2) 0 (k f r) plays the major role. This is because it describes the outward propagating spherical wave.…”

Section: Forced Acoustic Vibrationsmentioning

confidence: 99%

“…In the following it is assumed that F (x) = A h (2) 0 (k f r) and, to make the final results real, an intensity of the source A = 5.51 · 10 −3 is assumed. To omit the singularity of h (2) 0 (k f r) at r = 0, some space around the source is omitted; this is the cube space with dimensions 0.2 × 0.2 × 0.2 m. Finally, the sound pressure level L(x), through Eq. (47), is calculated.…”

Section: Numerical Calculationsmentioning

confidence: 99%

“…It requires an evaluation of eigenvalues of the Helmholtz equation assuming some boundary conditions imposed on the walls. Since the acoustic eigenvalue equation is complicated, the numerical method should be applied to find eigenvalues (Naka et al, 2005;Kuttruff, 2000;Bistafa, Morrissey, 2003), e.g. the Newton or bisection method.…”

Section: Introductionmentioning

confidence: 99%

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An Influence of the Wall Acoustic Impedance on the Room Acoustics. The Exact Solution

Brański

Kocan-Krawczyk

Prędka

2017

Archives of Acoustics

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The Fourier method is applied to the description of the room acoustics field with the combination of uniform impedance boundary conditions imposed on some walls. These acoustic boundary conditions are expressed by absorption coefficient values In this problem, the Fourier method is derived as the combination of three one-dimensional Sturm-Liouville (S-L) problems with Robin-Robin boundary conditions at the first and second dimension and Robin-Neumann ones at the third dimension. The Fourier method requires an evaluation of eigenvalues and eigenfunctions of the Helmholtz equation, via the solution of the eigenvalue equation, in all directions. The graphic-analytical method is adopted to solve it It is assumed that the acoustic force constitutes a monopole source and finally the forced acoustic field is calculated. As a novelty, it is demonstrated that the Fourier method provides a useful and efficient approach for a room acoustics with different values of wall impedances. Theoretical considerations are illustrated for rectangular cross-section of the room with particular ratio. Results obtained in the paper will be a point of reference to the numerical calculations.

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Section: Forced Acoustic Vibrationsmentioning

confidence: 99%

Section: Numerical Calculationsmentioning

confidence: 99%

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An Influence of the Wall Acoustic Impedance on the Room Acoustics. The Exact Solution

Brański

Kocan-Krawczyk

Prędka

2017

Archives of Acoustics

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“…Although, prediction difficulties at frequencies less than 100 Hz were found for relatively high absorption coefficients / low impedances configurations. Due to these limitations, the mathematics behind the Bistafa and Morrissey model [7] were adapted using a new numerical implementation to the analytical solution, so that the effect of increasing damping on the compliance of listening rooms could be investigated with greater precision.…”

Section: Previous Wave Based Room Prediction Modelsmentioning

confidence: 99%

Effects of damping on the low-frequency acoustics of listening rooms based on an analytical model

Dance

Buuren²

2013

Journal of Sound and Vibration

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“…Recent studies have been mainly focused on developing more effective root searching algorithms for finding eigensolutions. For instance, Bistafa and Morrissey [4] compared two different numerical procedures: one is the Newton's method and the other is referred to as the homotopic continuation technique based on the numerical integration of differential equations. The roots are searched for the cases from soft walls to the terminal impedance with small increments.…”

Section: Introductionmentioning

confidence: 99%

Acoustic Analysis of Enclosed Sound Space as well as Its Coupling with Flexible Boundary Structure

Du¹,

Liu²,

Liu³

2018

Computational and Experimental Studies of Acoustic Waves

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Combustion instability is often encountered in various power systems, a good understanding on the sound field in acoustic cavity as well as its coupling with boundary flexible structure will be of great help for the reliability design of such combustion system. An improved Fourier series method is presented for the acoustic/vibro-acoustic modelling of acoustic cavity as well as the panel-cavity coupling system. The structuralacoustic coupling system is described in a unified pattern using the energy principle. With the aim to construct the admissible functions sufficiently smooth for the enclosed sound space as well as the flexible boundary structure, the boundary-smoothed auxiliary functions are introduced to the standard multi-dimensional Fourier series. All the unknown coefficients and higher order variables are determined in conjunction with Rayleigh-Ritz procedure and differential operation term by term. Numerical examples are then presented to show the correctness and effectiveness of the current model. The model is verified through the comparison with those from analytic solution and other approaches. Based on the model established, the influence of boundary conditions on the acoustic and/or vibro-acoustic characteristics of the structural-acoustic coupling system is addressed and investigated.

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Numerical solutions of the acoustic eigenvalue equation in the rectangular room with arbitrary (uniform) wall impedances

Cited by 29 publications

References 3 publications

An Influence of the Wall Acoustic Impedance on the Room Acoustics. The Exact Solution

An Influence of the Wall Acoustic Impedance on the Room Acoustics. The Exact Solution

Effects of damping on the low-frequency acoustics of listening rooms based on an analytical model

Acoustic Analysis of Enclosed Sound Space as well as Its Coupling with Flexible Boundary Structure

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