带边角裂纹悬臂Mindlin板的振动特性研究

摘要

本文基于Mindlin板理论,应用Ritz法研究带边角裂纹Mindlin板的振动特性,分析了不同裂纹参数如裂纹位置,裂纹长度,裂纹角度对悬臂Mindlin板的固有频率和模态的影响.利用Ritz法求解固有频率和模态函数,本文构造了一个特殊的模态函数,其模态函数由两部分构成,一部分是用梁函数组合法得到的无裂纹理想完整矩形板的振型,另一部分是利用裂纹尖端奇异性理论,构造描述裂纹附近位移和转角不连续的角函数.通过高精度的数值计算软件Maple得出结果,并与有限元软件ANSYS分析的结果进行对比,验证本文计算结果的准确性.%This paper examines the natural frequencies and modes of cracked Mindlin plate using the Ritz method based on the Mindlin plate theory.The vibration characteristics of cantilever Mindlin plate with a side crack are presented,and the effect of the side crack on the natural frequencies and modal function of Mindlin plate is also investigated.In this analysis,a special mode shape function composed of two parts is employed,where one part is the ideal mode shape of intact Mindlin plate obtained by the beam function combination,and the other part is the comer function which uses the vertex singularity theory to construct the expression of deflection and rotation discontinuity along the crack.The results of the Mindlin theory obtained by a high-precision numerical software of Maple is then compared and verified against the data from finite element simulation by ANSYS.