The method of point matching proposed by Kang and Lee ͓J. Acoust. Soc. Am. 107, 1153-1160 ͑2000͔͒ is revisited. This method can be seen as a single-layer potential approach from the viewpoint of imaginary-part dual BEM developed by Chen et al. ͓J. Chin. Inst. Eng. 12, 729-739 ͑1999͔͒. Based on the concept of double-layer potential, an innovative method is proposed to deal with the problem of spurious eigensolution for the Neumann problem. Also, the acoustic mode is analytically derived for the circular cavity. Both the analytical study for a circular case and numerical result for a square cavity show the validity of the proposed formulation.

The paper is devoted to develop a new scheme to calculate impedance matrices for axial-symmetric foundations embedded in halfspace medium. The half-space medium can be approximated by increasing thickness of one layer stratum on rigid bedrock due to the effect of material damping. However, as thickness increases, the numerical problem will arise. This problem is caused by the numerical contamination by some negligible reflection waves from rigid bedrock. In reality, the effect of these reflection waves on impedance is getting small as the thickness of the one layer stratum increases. Therefore, the scheme will employ the solutions for one layer stratum with suppressing these reflection waves to generate the impedance for the case of half-space. The numerical results by the presented scheme are compared with the results by other scheme in order to show that the new numerical scheme is effective and the solutions in layered medium can be extended to obtain the results for the cases of layered half-space medium. Some numerical results of torsional, vertical, horizontal, coupling and rocking impedances with different embedded depths will be presented and comments on the numerical scheme will be given.

No abstract

No abstract

In this paper, we develop an ef®cient mixed-part dual BEM to solve the eigensolutions of a circular cavity analytically and numerically. The method is proposed by choosing a fewer number of equations from the dual BEM instead of all of the equations in the dual BEM developed by Chen and his coworkers. To solve this problem analytically, the spurious solution can be ®ltered out by adding constraints from the dual boundary integral equations. The proposed method is superior to the complex-valued BEM not only for half effort in constructing the in¯uence matrix, but also for its fewer size of dimension. Also, numerical experiments are performed to compare with the analytical results and the true eigensolutions can be easily extracted out in conjunction with the singular value decomposition technique (SVD). The optimum number of collocation point and appropriate collocating positions for the additional constraints are discussed.