不同位置四点支承矩形薄板的自由振动特性  

Free Vibrational Characteristics of Four-Point-Supported Rectangular Thin Plate with Different Supporting Locations

作　　者：李军委 鲍四元 沈峰 Li Junwei;Bao Siyuan;Shen Feng(Department of Engineering Mechanics,School of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China)

机构地区：[1]苏州科技大学土木工程学院工程力学系,苏州215011

出　　处：《动力学与控制学报》2023年第11期62-72,共11页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(51709194)。

摘　　要：研究不同位置四点支承条件下矩形薄板的自由振动特性.首先,在板结构模型的不同位置上引入横向约束弹簧,并设定人工弹簧的刚度值以模拟出四点支承的边界条件.然后,基于二维改进傅里叶级数表示结构的位移容许函数,其中改进部分的正弦附加项可解决以往位移函数在边界上可能存在的求导不连续问题.建立矩形板系统能量对应的泛函,令其取驻值建立线性方程组.最后,求解矩阵特征值问题得到点支承矩形板自由振动频率等参数,给出不同位置四点支承条件下矩形薄板的振动特性.所应用二维改进傅里叶级数法中,位移函数基于改进傅里叶级数展开时的附加项能够提高结果的精度和收敛速度.研究结果为不同位置点支承矩形板的自由振动问题提供一定的参考.The free vibration characteristics of rectangular thin plates with four-point supports at different locations are studied.Firstly,the lateral constraint springs are introduced at different locations of the plate structure model,and the stiffness values of artificial springs are set to simulate the boundary conditions of four-point supports.Then based on the two-dimensional modified Fourier series,the admissible displacement function of the structure is expressed,in which the additional terms of the improved parts can solve the discontinuity problem of the derivatives of the displacement function on the boundary.The energy functional of the rectangular plate system is established,and the linear equations are established by letting the functional choose the stationery value.Finally,the free vibration frequency parameters of the point-supported rectangular plate are obtained by solving matrix eigenvalue problems,and the vibration characteristics of the rectangular plate supported by four points at different positions are given.In the two-dimensional modified Fourier series method,the additional terms can improve the accuracy and rate of convergence.The research results provide some reference for the free vibration of rectangular plates supported at different points.

关 键 词：矩形薄板 点支承 自由振动 改进傅里叶级数法 

分 类 号：O343[理学—固体力学]