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| Direct perturbation method of nonlinear vibration for the elastic circular thin plate |
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| DOI：10.7511/jslx19984073 |
| KeyWord:direct perturbation method,calculus of variations,weighted integral |
| Huang Qingda |
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| Abstract: |
| In this paper, the nondimensional amplitud in the centre of the elastic circular thin plate and the ratio of the thickness to the radius are used as the parameters to expand the derivatives of the stress and deflection functions with respect to the radius and the frequency of the free vibration into dualparameter power series. Direct perturbation method is used to get every orders of recursive linear portial differential equations, and the variational method to get approximate solutions of these equations. Thus the fundamental formula of the nonlinear vibrations frequency about elastic circular thin plate is obtained. |
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