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| Analysis of nonlinear vibration of a functionally graded conical shell with simply support at four edges |
| Received:April 24, 2021 Revised:September 06, 2021 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20210424001 |
| KeyWord:functionally graded materials conical shell nonlinear vibration response |
| Author | Institution |
| 张宇航 |
南昌航空大学 航空制造工程学院, 南昌 |
| 刘文光 |
南昌航空大学 航空制造工程学院, 南昌 |
| 刘超 |
南昌航空大学 航空制造工程学院, 南昌 |
| 吕志鹏 |
南昌航空大学 航空制造工程学院, 南昌 |
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| Abstract: |
| The purpose of this article is to study the nonlinear free vibration of a functionally graded conical shell simply supported at its four edges.Firstly,the Voigt model and the power-law distribution function were employed to describe the physical properties of the FGMs.Subsequently,the energy expression of the functionally graded conical shell considering von-Karman geometric nonlinearity was established,and the equations of motion were derived by the Hamilton principle.Thereafter,the equations of motion of the conical shell were simplified into a single degree of freedom nonlinear differential equation by using the Galerkin method and only considering only the transverse vibration.In the end,the nonlinear vibration equation was solved by the improved L-P method and the Runge-Kutta method.And the nonlinear vibration responses of the shell were analysed and the effects of geometric parameters and ceramic volume fraction exponents on the nonlinear frequency responses of the shell were discussed.Results indicate that the geometric parameters have more effects on the nonlinear frequency and the vibration response than the ceramic volume fraction exponents;the geometric parameters and the ceramic volume fraction exponents affect the vibration response by affecting the frequency;the conical shell presents the nonlinear characteristics of a hardening spring. |