Acoustic eigenvalues of rectangular rooms with arbitrary wall impedances using the interval Newton∕generalized bisection method

Naka, Yusuke; Oberai, Assad A.; Shinn‐Cunningham, Barbara

doi:10.1121/1.2114607

Cited by 28 publications

(25 citation statements)

References 11 publications

(17 reference statements)

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“…(36). In practice, instead of the acoustic potential, the acoustic pressure and secondary acoustic quantities play a major role.…”

Section: Forced Acoustic Vibrationsmentioning

confidence: 99%

“…The Fourier method belongs to exact ones and it may be used for solving boundary problems of the room acoustics (Blackstock, 2000;Kuttruff, 2000), being inherent to the modal analysis (Naka et al, 2005). It requires an evaluation of eigenvalues of the Helmholtz equation assuming some boundary conditions imposed on the walls.…”

Section: Introductionmentioning

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%

See 2 more Smart Citations

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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“…(36). In practice, instead of the acoustic potential, the acoustic pressure and secondary acoustic quantities play a major role.…”

Section: Forced Acoustic Vibrationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Other options different from these normal modes are available in the literature. In [22] a set of eigenfunctions adapted in order to satisfy the absorbing (Robin) boundary conditions imposed on the walls by means of acoustic impedances is presented. Another example of enriched modal basis can be found in [36] where the classical functions are combined with the free field Green's function in order to improve the precision of the interpolation (specially around the point sound source) and reduce the number of functions to be used.…”

Section: Pressure Field Inside Roomsmentioning

confidence: 99%

Modal-based prediction of sound transmission through slits and openings between rooms

Poblet-Puig

Ferran

2013

Journal of Sound and Vibration

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The transmission of sound through slits and openings between cuboid-shaped rooms is analysed. A deterministic model that describes the pressure fields inside the rooms in terms of eigenfunctions and uses the Dirichlet-to-Neumann technique in order to reproduce the slit effect is presented. An efficient formulation of the problem is obtained thanks to the splitting of the original domain into three domains: sending room, slit, receiving room. The geometry and boundary conditions of the problem can be modelled in detail like in an element-based numerical technique (such as the finite element method) but with smaller computational costs. The model is compared with numerical solutions, existent models and published experimental data. Afterwards it is used to analyse some aspects such as the influence of slit dimensions, opening position, room properties (dimensions and absorption) that cannot be taken into account with the available models. These usually suppose that the slit or opening connects two unbounded acoustic domains.

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“…They found that the latter procedure is much faster in finding all the possible roots. Naka et al [5] utilized an interval Newton/generalized bisection (IN/GB) method to find the roots of the non-linear characteristic equation within any given interval for the modal analysis of rectangular room with arbitrary wall impedances.…”

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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Acoustic eigenvalues of rectangular rooms with arbitrary wall impedances using the interval Newton∕generalized bisection method

Cited by 28 publications

References 11 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

Modal-based prediction of sound transmission through slits and openings between rooms

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

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