Panel Contribution Analysis Based on FEM, BEM and Numerical Green’s Function Approaches

The panel acoustic contribution analysis is used to determine the contribution of vibrating panels to the noise level inside closed spaces like a car cabin. The use of numerical techniques makes it possible to rate the panels according to their contributions accounting for the interaction between the structural vibrations and the acoustic pressure at a listening point. We consider the application of the finite and boundary element methods and the numerical Green’s function approaches to the problem and discuss the pros and cons regarding their use. The results show that the numerical Green’s function approach coupled to structure can be effectively used for the panel contribution analysis in situations with multiple panels and few listening points.

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One‐way versions of the Kirchhoff Integral

Geophysics ◽

10.1190/1.1442672 ◽

1989 ◽

Vol 54 (4) ◽

pp. 460-467 ◽

Cited By ~ 29

Author(s):

A. J. Berkhout ◽

C. P. A. Wapenaar

Keyword(s):

Boundary Conditions ◽

Green’S Function ◽

Wave Field ◽

Green's Function ◽

Green's Functions ◽

Acoustic Pressure ◽

Green’S Functions ◽

Absorbing Boundary Conditions ◽

Multiple Reflections ◽

Kirchhoff Integral

The conventional Kirchhoff integral, based on the two‐way wave equation, states how the acoustic pressure at a point A inside a closed surface S can be calculated when the acoustic wave field is known on S. In its general form, the integrand consists of two terms: one term contains the gradient of a Green’s function and the acoustic pressure; the other term contains a Green’s function and the gradient of the acoustic pressure. The integrand can be simplified by choosing reflecting boundary conditions for the two‐way Green’s functions in such a way that either the first term or the second term vanishes on S. This conventional approach to deriving Rayleigh‐type integrals has practical value only for media with small contrasts, so that the two‐way Green’s functions do not contain significant multiple reflections. We present a modified approach for simplifying the integrand of the Kirchhoff integral by choosing absorbing boundary conditions for the one‐way Green’s functions. The resulting Rayleigh‐type integrals are the theoretical basis for true amplitude one‐way wave‐field extrapolation techniques in inhomogeneous media with significant contrasts.

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Three-dimensional Green's function and its derivative for materials with general anisotropic magneto-electro-elastic coupling

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2009.0389 ◽

2009 ◽

Vol 466 (2114) ◽

pp. 515-537 ◽

Cited By ~ 37

Author(s):

Federico C. Buroni ◽

Andrés Sáez

Keyword(s):

Green’S Function ◽

Green's Function ◽

Numerical Stability ◽

Three Dimensional ◽

Transversely Isotropic ◽

Boundary Element Methods ◽

Stroh Formalism ◽

Elastic Coupling ◽

First Order ◽

Explicit Expressions

Explicit expressions of Green’s function and its derivative for three-dimensional infinite solids are presented in this paper. The medium is allowed to exhibit a fully magneto-electro-elastic (MEE) coupling and general anisotropic behaviour. In particular, new explicit expressions for the first-order derivative of Green’s function are proposed. The derivation combines extended Stroh formalism, Radon transform and Cauchy’s residue theory. In order to cover mathematical degenerate and non-degenerate materials in the Stroh formalism context, a multiple residue scheme is performed. Expressions are explicit in terms of Stroh’s eigenvalues, this being a feature of special interest in numerical applications such as boundary element methods. As a particular case, simplifications for MEE materials with transversely isotropic symmetry are derived. Details on the implementation and numerical stability of the proposed solutions for degenerate cases are studied.

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Transmission loss of lined Helmholtz resonator with annular air gap: A Green's function based approach

Noise Control Engineering Journal ◽

10.3397/1/376912 ◽

2021 ◽

Vol 69 (2) ◽

pp. 112-121

Author(s):

D. Veerababu ◽

B. Venkatesham

Keyword(s):

Green’S Function ◽

Transfer Matrix ◽

Green's Function ◽

Acoustic Pressure ◽

Velocity Potential ◽

Transmission Loss ◽

Numerical Models ◽

Cumulative Effect ◽

Helmholtz Resonator ◽

Air Gap

The present article discusses a Green's function-based semi-analytical method to predict the transmission loss of a lined Helmholtz resonator with annular air gap. In the analysis, the walls of the chamber are assumed to be acoustically rigid except at the neck portion where it is treated as a piston source moving with uniform velocity. The Green's function is developed as the summation of eigenfunctions of the central duct. The cumulative effect of the lined portion and the annular air gap including the perforated screens is incorporated as the reflection coefficient in the eigenfunctions. By using the Kirchhoff-Helmholtz integral equation, the velocity potential generated by the piston inside the chamber is evaluated. A transfer matrix relating the acoustic pressure and volume velocity across the neck in the main duct is formulated. The effect of the neck length is included as an added inertance to the impedance in the transfer matrix. The results obtained from the proposed method are validated with the developed numerical models and the experimental data available in the literature. A parametric study has been conducted to investigate the effect of porosity of the perforated screens, thickness and flow resistivity of the absorptive material on the transmission loss of the chamber.

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