弹性地基上任意边界条件矩形中厚板的振动特性分析  

Vibration Behavior Analysis of Rectangular Thick Plates with Arbitrary Boundary Conditions on Elastic Foundation

作　　者：丁凯文 高芳清[1] 郑双星 DING Kaiwen;GAO Fangqing;ZHENG Shuangxing(School of Mechanics and Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]西南交通大学力学与工程学院,成都610031

出　　处：《四川轻化工大学学报（自然科学版）》2021年第3期69-76,共8页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金项目(11872139)。

摘　　要：基于Mindlin理论研究了矩形中厚板在考虑Winkler地基模型时任意边界条件下的振动特性。在板的四周边上施加旋转约束弹簧、扭转约束弹簧及横向位移约束弹簧,通过改变相应弹簧的刚度系数以模拟任意约束边界。结合Hamilton原理及变分以建立地基板整体结构控制方程的矩阵形式,利用添加了辅助项的改进Fourier级数法,使得位移函数和两个转角函数的一阶偏导在整个中厚板的求解域内都连续,以满足任意边界条件。通过算例分析并与已有文献值比对,最大误差不超过1%,本方法的收敛性与准确性得以验证。在此基础上进一步研究了约束弹簧刚度系数、板尺寸参数和地基基床系数对结构频率的影响规律。Based on the Mindlin theory,the free vibration characteristics of rectangular thick plates on Winkler foundation with arbitrary boundary conditions are studied.The lateral displacement spring,rotation spring and torsion spring are set on the four sides of the plate.The stiffness coefficient of the corresponding spring is changed to simulate any boundary constraint.Based on Hamilton’s principle and variation,the matrix of the governing equation of the whole structure of the ground plate is established.By using the improved Fourier-series method,the displacement function and rotation function are continuous to satisfy any elastic boundary condition in the whole solution domain.By comparison with other literatures,the results show that the maximum error is no more than 1%.So the convergence and accuracy of this method are tested.The effects of the structural frequency and the constraint stiffness coefficients,the foundation coefficient and the sheet size parameters are explored further.

关 键 词：WINKLER地基 Mindlin理论 矩形中厚板 任意边界 改进Fourier级数 HAMILTON原理 

分 类 号：O327[理学—一般力学与力学基础]