Quasi-Green’s Function Method for Free Vibration of Clamped Thin Plates on Winkler Foundation

LI Shan-qing; YUAN Hong

doi:10.3879/j.issn.1000-0887.2011.03.001

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LI Shan-qing, YUAN Hong. Quasi-Green’s Function Method for Free Vibration of Clamped Thin Plates on Winkler Foundation[J]. Applied Mathematics and Mechanics, 2011, 32(3): 253-262. doi: 10.3879/j.issn.1000-0887.2011.03.001

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Quasi-Green’s Function Method for Free Vibration of Clamped Thin Plates on Winkler Foundation

doi: 10.3879/j.issn.1000-0887.2011.03.001

MOE Key Laboratory of Disaster Forecast and Control in Engineering, Institute of Applied Mechanics, Jinan University, Guangzhou 510632, P. R. China

Received Date: 2010-09-27
Rev Recd Date: 2011-01-14
Publish Date: 2011-03-15

Abstract

Abstract

The quasi-Green's function method was employed to solve the free vibration problem of clamped thin plates on Winkler foundation.A quasi-Green's function was 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 free vibration problem of clamped thin plates on Winkler foundation was reduced to Fredholm integral equations of the second kind by Green formula.Irregularity of the kernel of integral equation was overcome by choosing a suitable form of the normalized boundary equation.Numerical results show high accuracy of the method given by the present paper,and it is an effective mathematical method.
- Green function,
- integral equation,
- clamped thin plates,
- Winkler foundation,
- free vibration

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References(26)

References

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