混合边界约束多层矩形薄板的自由振动解析解研究  

Analytical study of free vibration for layered rectangular plate with mixed boundary conditions

作　　者：王春玲[1] 赵鲁珂 刘韡[1] Wang Chunling;Zhao Luke;Liu Wei(School of Science,Xi’an University of Architecture&Technology,710055,Xi’an,China)

机构地区：[1]西安建筑科技大学理学院

出　　处：《应用力学学报》2020年第1期390-396,I0027,I0028,共9页Chinese Journal of Applied Mechanics

基　　金：陕西省教育厅专项科研基金(2014JK1394)

摘　　要：构造带有补充项的双重正弦傅里叶级数作为振型函数通解,来研究混合边界约束多层矩形薄板的自由振动特性。考虑振型函数中待定常数的物理意义,再结合多层矩形薄板的边界条件,简化得到了具体混合边界约束多层矩形薄板的振型函数。结合控制方程、未用的边界条件和协调条件,建立了求解频率的解析方程组,将其转化为广义特征值问题求其量纲为一的频率。选取参数计算并与文献结果进行了对比,二者吻合良好,证明了本文所采用方法以及提出通解的正确性。该通解不但可以满足多层矩形薄板的任意边界约束条件,而且其中的各个待定常数具有明确的物理意义,同时该通解也能用于研究多层矩形薄板的弯曲和稳定问题,从而使得多层矩形薄板问题的求解简单化、统一化、规律化。A double sine Fourier series with supplementary terms function is proposed to investigate layered rectangular plate with mixed boundary conditions.Simplified function for layered rectangular plate is derived by considering boundary conditions and the physical meanings of constants in original function.Equation system,which contains governing equations,remaining boundary conditions,compatibility conditions for public boundary,is converted to a generalized eigenvalue problem to calculate the non-dimensional frequencies.A sample is tested and the results are close to published data,which verifies the correctness of derivation and proposed function.The proposed function,whose constants contains certain physical meanings,could conveniently investigates free vibration problem of layered rectangular plate with arbitrary boundary conditions,even bending problem and stability problem for layered rectangular plates.Therefore,the method in this paper could unify the solution and simplify the approach for the study of layered rectangular plate with mixed boundary conditions.

关 键 词：多层矩形薄板 混合边界约束 双重级数 自由振动 解析研究 

分 类 号：O321[理学—一般力学与力学基础]