On the formulation of the acoustic boundary element eigenvalue problems

Abstract

SUMMARYAcoustic 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 (aP/an = 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.

The Boundary Element Method in Acoustics

“…The method seems to have the advantage of the finite element method in that a linear eigenvalue problem results and the advantage of the boundary element method in that a solution on the boundary only is sought in the main computation. The method is considered further in references [24], [2].…”

“…In the second test the Neumann mode is sought in the range [2,3]. The program returns three results 2.4068, 2.4071 and 2.3163.…”

“…In the second test problem the Neumann modes are sought in the range [2,4] with NK=4 (cubic interpolation). The approximations 2.089 and 3.360 are found to the exact solutions of 2.082 and 3.342.…”

On DR/BEM for eigenvalue analysis of 2-D acoustics

“…However, despite the abovementioned general applicability of the DR/BEM, several concerns were reported when it was applied to the extraction of eigenvalues in acoustic cavities (Provatidis 1987;Kanarachos and Provatidis 1987;Coyette and Fyfe 1990;Ali et al 1991Ali et al ,1995Provatidis and Kanarachos 1995). Trying to explain this shortcoming, it was hypothesized that higher harmonics appearing in acoustics probably make a difference.…”

Earthquake‐induced hydrodynamic pressures on a 3D rigid dam–reservoir system using DRBEM and a radiation matrix

“…This method has proven to be an e ective tool in the solution of free vibration elasticity problems [13,14] and acoustic eigenvalues analysis [15,16]. Tsai et al [17] have applied the method successfully to model a twodimensional dam-reservoir interaction problem.…”