直接Trefftz边界元法在薄膜自由振动问题中的应用。

Applications of the direct Trefftz boundary element method to the free-vibration problem of a membrane.

作者信息

Chang Jiang Ren, Liu Ru Feng, Yeih Weichung, Kuo Shyh Rong

机构信息

Department of System Engineering and Naval Architecture, National Taiwan Ocean University, Keelung, Republic of China.

出版信息

J Acoust Soc Am. 2002 Aug;112(2):518-27. doi: 10.1121/1.1494992.

DOI:10.1121/1.1494992

PMID:12186033

Abstract

In this paper, the direct Trefftz method is applied to solve the free-vibration problem of a membrane. In the direct Trefftz method, there exists no spurious eigenvalue. However, an ill-posed nature of numerical instability encountered in the direct Trefftz method requires some treatments. The Tikhonov's regularization method and generalized singular-value decomposition method are used to deal with such an ill-posed problem. Numerical results show the validity of the current approach.

摘要

本文将直接Trefftz方法应用于求解薄膜的自由振动问题。在直接Trefftz方法中，不存在虚假特征值。然而，直接Trefftz方法中遇到的数值不稳定性的不适定性质需要一些处理。采用Tikhonov正则化方法和广义奇异值分解方法来处理这种不适定问题。数值结果表明了当前方法的有效性。