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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (3): 265-276.doi: https://doi.org/10.1007/s10483-011-1412-x

• Articles •    下一篇

Quasi-Green’s function method for free vibration of clamped thin plates on Winkler foundation

李善倾，袁鸿   

  1. Institute of Applied Mechanics, Key Laboratory of Disaster Forecast and Control in Engineering of Ministry of Education of China, Jinan University, Guangzhou 510632, P. R. China
  • 收稿日期:2010-09-27 出版日期:2011-02-28 发布日期:2011-03-01

Quasi-Green’s function method for free vibration of clamped thin plates on Winkler foundation

LI Shan-Qing, YUAN Hong   

  1. Institute of Applied Mechanics, Key Laboratory of Disaster Forecast and Control in Engineering of Ministry of Education of China, Jinan University, Guangzhou 510632, P. R. China
  • Received:2010-09-27 Online:2011-02-28 Published:2011-03-01

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摘要： The quasi-Green’s function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green’s function is established by the fundamental solution and the boundary equation of the problem. The function satisfies the homogeneous boundary condition of the problem. The mode-shape differential equation of the free vibration problem of clamped thin plates on the Winkler foundation is reduced to the Fredholm integral equation of the second kind by Green’s formula. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The numerical results show the high accuracy of the proposed method.

Abstract: The quasi-Green’s function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green’s function is established by the fundamental solution and the boundary equation of the problem. The function satisfies the homogeneous boundary condition of the problem. The mode-shape differential equation of the free vibration problem of clamped thin plates on the Winkler foundation is reduced to the Fredholm integral equation of the second kind by Green’s formula. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The numerical results show the high accuracy of the proposed method.

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