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On the formulation of the acoustic boundary element eigenvalue problems
Author(s) -
Ali Ashraf,
Rajakumar C.,
Yunus Shah M.
Publication year - 1991
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620310704
Subject(s) - boundary element method , eigenvalues and eigenvectors , mathematics , reciprocity (cultural anthropology) , algebraic number , algebraic equation , matrix (chemical analysis) , boundary value problem , mathematical analysis , finite element method , mathematical optimization , engineering , structural engineering , physics , psychology , social psychology , materials science , quantum mechanics , nonlinear system , composite material
Acoustic algebraic eigenvalue analysis by the Boundary Element Method (BEM) can be formulated by the Dual Reciprocity Method (DRM) of Nardini and Brebbia or by the Complementary Function‐Particular Integral Method (PIM) proposed by Ahmad and Banerjee. But both DRM and PIM require inversion of a matrix of size at least as large as the system matrices before the equations can be cast in the form of generalized eigensystem. This makes these methods inefficient for large problems of practical interest. In this paper, a rather simple technique is proposed which eliminates the need to invert any matrix in the process of setting up the algebraic eigenvalue problem, especially for the most important case where all the boundary walls are acoustically hard (∂ P /∂ n = 0). A few example problems having known analytical and experimental results are solved in order to demonstrate the validity of the new technique. It is also demonstrated that, unlike in elasticity, here the boundary element domain must be adequately zoned or an adequate number of internal points must be incorporated in order to solve truly 2‐D or 3‐D problems.