波纹圆薄板的非线性振动
Non-Linear Vibration of Circular Corrugated Piates
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摘要: 本文首先用最小作用量原理推导出波纹圆薄板的变分方程。选取波纹圆薄板中心最大振幅为摄动参数,采用摄动变分法,一次近似求得了波纹板线性振动时的固有频率,继之求得了波纹板的非线性固有频率。通过和线性结果比较,证实了本文的尝试是可行的。Abstract: In this paper, first by using Hamilton principle, we derive the variational equation of circular corrugated plates. Taking the central maximum amplitude of circular corrugated plates as the perturbation parameter and adopting the perturbation variational method, in the first-order approximation, we obtain the natural frequency of linear vibration of circular corrugated plates and then the nonlinear natural frequency of the corrugated plates. By comparing with the linear results, the attempt of this paper is proved feasible.
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