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

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.