Improved non-dimensional dynamic influence function method for vibration analysis of arbitrarily shaped plates with clamped edges

Sang Wook Kang, Satya N. Atluri

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

A new formulation for the non-dimensional dynamic influence function method, which was developed by the authors, is proposed to efficiently extract eigenvalues and mode shapes of clamped plates with arbitrary shapes. Compared with the finite element and boundary element methods, the non-dimensional dynamic influence function method yields highly accurate solutions in eigenvalue analysis problems of plates and membranes including acoustic cavities. However, the non-dimensional dynamic influence function method requires the uneconomic procedure of calculating the singularity of a system matrix in the frequency range of interest for extracting eigenvalues because it produces a non-algebraic eigenvalue problem. This article describes a new approach that reduces the problem of free vibrations of clamped plates to an algebraic eigenvalue problem, the solution of which is straightforward. The validity and efficiency of the proposed method are illustrated through several numerical examples.

Original languageEnglish
Pages (from-to)1-8
Number of pages8
JournalAdvances in Mechanical Engineering
Volume8
Issue number3
DOIs
StatePublished - Mar 2016

Keywords

  • Non-dimensional dynamic influence function method
  • algebraic eigenvalue problem
  • arbitrarily shaped plate
  • free vibration
  • mode shape
  • natural frequency

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