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
Citation: 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

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

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