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Applied Mathematics and Mechanics

, Volume 28, Issue 7, pp 847–853 | Cite as

Green quasifunction method for vibration of simply-supported thin polygonic plates on Pasternak foundation

  • Yuan Hong  (袁鸿)Email author
  • Li Shan-qing  (李善倾)
  • Liu Ren-huai  (刘人怀)
Article

Abstract

A new numerical method—Green quasifunction is proposed. The idea of Green quasifunction method is clarified in detail by considering a vibration problem of simply-supported thin polygonic plates on Pasternak foundation. A Green quasifunction is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The mode shape differential equation of the vibration problem of simply-supported thin plates on Pasternak foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the Green quasifunction method.

Key words

Green function integral equation vibration of thin plates Pasternak foundation 

Chinese Library Classification

O241.8 TU471.2 

2000 Mathematics Subject Classification

34B27 74K20 

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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Yuan Hong  (袁鸿)
    • 1
    Email author
  • Li Shan-qing  (李善倾)
    • 1
  • Liu Ren-huai  (刘人怀)
    • 1
  1. 1.Institute of Applied MechanicsJinan UniversityGuangzhouP. R. China

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