Numerical implementation of the lumped parameter model for the acoustic power output of a vibrating structure

In a previous paper, a lumped parameter model for the acoustic radiation from a vibrating structure was defined by dividing the surface of the structure into elements, expanding the acoustic field from each of the elements in a multipole expansion, and truncating all but the lowest-order terms in the expansion. Here, the lumped parameter model is implemented numerically by requiring the boundary condition for the normal surface velocity to be satisfied in a lumped parameter sense. This alleviates the difficulties typically encountered in enforcing the boundary condition, leading to a relatively simple numerical solution with well-defined convergence properties. The basis functions for the numerical analysis are taken as the acoustic fields of discrete simple, dipole, and tripole sources located at the geometrical centers of the surface elements. The different source types are used to represent the radiation from different kinds of surface elements: simple sources for elements in the plane of an infinite b...

[1]  J. B. Fahnline,et al.  A numerical solution for the general radiation problem based on the combined methods of superposition and singular‐value decomposition , 1991 .

[2]  L. J. Gray,et al.  On the treatment of corners in the boundary element method , 1990 .

[3]  F. J. Rizzo,et al.  A weakly singular form of the hypersingular boundary integral equation applied to 3-D acoustic wave problems , 1992 .

[4]  G. R. Cowper,et al.  Gaussian quadrature formulas for triangles , 1973 .

[5]  H. A. Schenck.  Improved Integral Formulation for Acoustic Radiation Problems , 1968 .

[6]  Ismael Herrera,et al.  Trefftz method: Fitting boundary conditions , 1987 .

[7]  D. Schweikert,et al.  Sound Radiation from an Arbitrary Body , 1963 .

[8]  H. Levine,et al.  Output of acoustical sources , 1980 .

[9]  R. B. Nelson,et al.  Consistent Formulation of Sound Radiation From Arbitrary Structure , 1975 .

[10]  David S. Burnett,et al.  A three‐dimensional acoustic infinite element based on a prolate spheroidal multipole expansion , 1994 .

[11]  P.J.T. Filippi,et al.  Layer potentials and acoustic diffraction , 1977 .

[12]  P. S. Han,et al.  An adaptive boundary element method , 1987 .

[13]  L. G. Copley,et al.  Integral Equation Method for Radiation from Vibrating Bodies , 1967 .

[14]  R. Kress,et al.  On the condition number of boundary integral operators for the exterior Dirichlet problem for the Helmholtz equation , 1983 .

[15]  Jeong-Guon Ih,et al.  Reactive characteristics of partial screens for a sound source mounted in an infinite baffle , 1995 .

[16]  C. Bouwkamp.  Theoretical and numerical treatment of diffraction through a circular aperture , 1970 .

[17]  L. G. Copley,et al.  Fundamental Results Concerning Integral Representations in Acoustic Radiation , 1968 .

[18]  J. Hwang,et al.  A retracted boundary integral equation for exterior acoustic problem with unique solution for all wave numbers , 1991 .

[19]  L. J. Gray,et al.  A Hermite interpolation algorithm for hypersingular boundary integrals , 1993 .

[20]  George Chertock,et al.  Sound Radiation from Vibrating Surfaces , 1963 .

[21]  T. Terai.  On calculation of sound fields around three dimensional objects by integral equation methods , 1980 .

[22]  G. F. Miller,et al.  The application of integral equation methods to the numerical solution of some exterior boundary-value problems , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[23]  J. B. Fahnline,et al.  A lumped parameter model for the acoustic power output from a vibrating structure , 1996 .

[24]  T. W. Wu.  A direct boundary element method for acoustic radiation and scattering from mixed regular and thin bodies , 1995 .