A finite element method perturbation expansion for a coupled structural-acoustic system: two dimensional case
L. Deng, W. Boukaram, and C. Douglas
Japan Journal of Industrial and Applied Mathematics, 30, pp. 545-563, (2013)
The structural acoustic coupled vibration problem is very important in many engineering applications such as quality control of vehicles. Formulating the problem using the finite element method leads to a nonsymmetric generalized eigenvalue problem. We show that the problem can be reformulated into uncoupled structural and acoustic problems by introducing a coupling strength parameter ε as a multiplier applied to the off-diagonal coupling terms. The discretized uncoupled problems then lead to a pair of symmetric generalized eigenvalue problems which can be efficiently and independently solved. The solutions of the uncoupled problems are then used to compute the coupled solution using the perturbation method and the introduced coupling strength parameter. We confirm the adequacy of the method by investigating numerical examples for a two dimensional uniform mesh, whose exact solution is known, as well as arbitrary meshes for a car-like example.
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