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Applied Mathematics and Mechanics

, Volume 17, Issue 8, pp 773–779 | Cite as

An analytical solution of transverse vibration of rectangular plates simply supported at two opposite edges with arbitrary number of elastic line supports in one way

  • Zhou Ding
Article
  • 52 Downloads

Abstract

This paper presents a new analytical solution of transverse vibration of rectangular plates simply supported at two opposite edges with arbitrary number of elastic line supports in one way. The reaction forces of the elastic line supports are regarded as the unknown external forces acted on the plate. The analytical solution of the differential equation of motion of the rectangular plate, which includes the unknown reaction forces, is gained. The frequency equation is derived by using the linear relutionships between the reaction forces of the elastic line supports and the transverse displacements of the plate along the elastic line supports. The representations of the frequency equation and the mode shape functions are different from those obtained by other methods.

Key words

rectangular plate eigen-frequency elastic line support analytical solution 

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References

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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Zhou Ding
    • 1
  1. 1.Nanjing University of Science and TechnologyNanjingP. R. China

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