LSFD method for accurate vibration modes and modal stress-resultants of freely vibrating plates that model VLFS

C. M. Wang, W. X. Wu, C. Shu, T. Utsunomiya

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

The Ritz method and some finite element formulations fail to furnish accurate modal stress-resultants for vibrating plates with free edges, even though the natural frequencies and mode shapes are accurately obtained. For example, by using the Ritz method, it was found that the modal twisting moments and shear forces violate the natural boundary conditions and that they contain erroneous "oscillations". This paper presents the least squares finite difference (LSFD) method for solving the freely vibrating plate problem. It will be shown herein that the modal stress-resultants obtained by the LSFD method satisfy the natural boundary conditions at the free edges without any oscillations.

Original languageEnglish
Pages (from-to)2329-2339
Number of pages11
JournalComputers and Structures
Volume84
Issue number31-32
DOIs
Publication statusPublished - Dec 1 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Modelling and Simulation
  • Materials Science(all)
  • Mechanical Engineering
  • Computer Science Applications

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