带圆开孔的弹性约束适度椭圆板的自由振动分析

Analysis of Free Vibration of Elastic Constrained Moderately Elliptical Plates with a Concentric Circular Core

采用弹性理论并结合边界摄动技术,对带中心圆孔的适度椭圆薄板的自由振动基频进行了分析.当薄板的内边界受弹性约束,外边界为自由,导出了自由振动基频的解析解.同时,利用ANSYS软件进行了数值模拟,通过经典边界条件下基频结果的对比,验证了基于本文理论解的计算结果的精确性.本方法可以有效用于处理具有曲线边界的薄板结构的自由振动问题.

Based on the elasticity theory and perturbation technique for boundary shape,the fundamental frequency of the natural vibration of a moderately elliptical plate with a concentric circular core was analyzed. When the plate was elastically constrained at the inner edge and was free at the outer edge,an analytical solution for the fundamental frequency of the natural vibration was derived. Meanwhile,numerical simulation was also performed by using the ANSYS code,and the comparison of the results for the fundamental frequency under classical boundary conditions testified the exactness of the computation based on the theoretical solution proposed in this paper. The present method can be used effectively to tackle the problem of free vibration of thin plate structures with curved boundary.