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Applied Mathematics and Mechanics (English Edition) ›› 1996, Vol. 17 ›› Issue (8): 773-779.

• 论文 • 上一篇    下一篇

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

周叮   

  1. Nanjing University of Science and Technology, Nanjing 210014, P. R. China
  • 收稿日期:1994-08-07 修回日期:1996-03-11 出版日期:1996-08-18 发布日期:1996-08-18
  • 基金资助:
    Project supported by the Science Foundation of Nanjing University of Science and Technology

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   

  1. Nanjing University of Science and Technology, Nanjing 210014, P. R. China
  • Received:1994-08-07 Revised:1996-03-11 Online:1996-08-18 Published:1996-08-18
  • Supported by:
    Project supported by the Science Foundation of Nanjing University of Science and Technology

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摘要： This paper presents presents a new analytical solution of transverse vibration ofrectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way. The reaction forces of the elastic line supports areregarded as foe unknown external forces acted on the plate. The analytical solution ofthe differential equation of motion of the rectangular plate, which includes theunknown reaction forces. is gained. The frequency’ equation is derived by using thelinear relationships between the reaction forces of the elastic line supports and thetransverse displacements of the plale along the elastic line supports. Therepresentations of foe frequency equation and the mode shape functions are differentfrom those obtained by other methods.

关键词: rectangular plate, eigen-frequency, elastic line support, analyticalSolution

Abstract: This paper presents presents a new analytical solution of transverse vibration ofrectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way. The reaction forces of the elastic line supports areregarded as foe unknown external forces acted on the plate. The analytical solution ofthe differential equation of motion of the rectangular plate, which includes theunknown reaction forces. is gained. The frequency’ equation is derived by using thelinear relationships between the reaction forces of the elastic line supports and thetransverse displacements of the plale along the elastic line supports. Therepresentations of foe frequency equation and the mode shape functions are differentfrom those obtained by other methods.

Key words: rectangular plate, eigen-frequency, elastic line support, analyticalSolution

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