Application for a Novel Perturbation Expansion Method

We formulate a coupled vibration problem between a structure and an acoustic field by FEM (finite element methods). The problem leads to a nonstandard eigenvalue problem. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the non-diagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with respect to ε which enables us to express the eigenpair for the coupled case by those for the decoupled case. In some practical applications, by using this perturbation series, it would become unnecessary to perform time consuming computations to get coupled eigenvalues, and hence the present results obtained by the perturbation analysis might have considerable engineering importance. We confirm the adequacy of this perturbation analysis by investigating numerical examples. The results are given for a two dimensional coupled problem which given exact solution so that we can compare the results.