A finite element method perturbation expansion for a coupled structural-acoustic system: two dimensional case

  • Li Deng
  • Wajih-Halim Boukaram
  • Craig C. Douglas
Original Paper Area 1


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 \({\varepsilon}\) 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.


Perturbation expansion Orthogonalization condition Car model FEM 

Mathematics Subject Classification

65 Numerical analysis 65z05 Applications to physics 


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Copyright information

© The JJIAM Publishing Committee and Springer Japan 2013

Authors and Affiliations

  • Li Deng
    • 1
  • Wajih-Halim Boukaram
    • 2
  • Craig C. Douglas
    • 3
  1. 1.Department of MathematicsUniversity of WyomingDept. 3036 LaramieUSA
  2. 2.King Abdullah University of Science and TechnologyThuwalKingdom of Saudi Arabia
  3. 3.School of Energy Resources and Department of MathematicsUniversity of WyomingDept. 3036 LaramieUSA

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