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| Received:December 23, 2014 Revised:May 09, 2015 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201602006 |
| KeyWord:the effect of both initial in-plane and transverse loads plate natural frequency finite plate element approximate solution |
| Author | Institution |
| 刘德贵 |
西南科技大学 土木工程与建筑学院, 绵阳 |
| 周世军 |
重庆大学 土木工程学院, 重庆 |
| 王宁 |
西南科技大学 土木工程与建筑学院, 绵阳 |
| 张春涛 |
西南科技大学 土木工程与建筑学院, 绵阳 |
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| Abstract: |
| Firstly,the strain energy expression,the dynamic equilibrium differential equation and the element stiffness matrix are presented for plates considering the effect of both initial in-plane and transverse loads via the energy variation principle.Then,the approximate solutions of fundamental frequencies for four typical plates,considering the effect of both initial in-plane and transverse loads,are derived by the Galerkin method,based on the dynamic equilibrium differential equation.And the approximate solutions of the first three frequencies for a simply supported rectangular plate,considering the effect of both initial in-plane and transverse loads,are solved by the Rayleigh method.The frequencies obtained by the finite plate element agree well with the approximate solutions,the reliability and efficiency of the presented finite plate element and those frequency approximate solutions are verified.Finally,the frequencies of plates influenced by the effect of both initial in-plane and transverse loads and related factors are analyzed by numerical examples,result shows that the key physical factors governing the effect of initial loads on the frequencies of plates are the initial loads (both in-plane and transverse),thickness and boundary condition etc.The effect of both initial in-plane and transverse loads on fundamental frequency is more remarkable than that on high-order frequencies.The frequencies influenced by initial in-plane loads and initial transverse loads respectively follow the linear pattern and the parabolic pattern. |
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