基于Walsh级数法层合梁自由振动分析  

Free vibration analysis of laminated beam with WSM

作　　者：郭诗白 胡平[1] 黎胜[1] GUO Shi-bai;HU Ping;LI Sheng(School of Mechanics and Aerospace Engineering,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学力学与航空航天学院,大连116024

出　　处：《计算力学学报》2024年第4期775-780,共6页Chinese Journal of Computational Mechanics

摘　　要：本文提出了一种基于Walsh级数离散化方法(WSM)的频率求解方法,对具有一般边界条件的层合梁进行了自由振动分析.采用考虑剪切效应和转动惯量的一阶剪切变形理论建立了层合梁理论模型,采用边界权重参数等效一般边界条件.以Walsh级数作为基函数离散位移最高阶导数再进行积分,由边界条件确定这一过程中产生的积分常数.将离散后的位移与转角代入控制方程转化为单变量线性方程.在此基础上,通过求解线性代数方程,可以得到复合材料层合梁的频率.对照现有文献计算结果,得到WSM法具有较好的收敛性和精度的结论.A Walsh series Discretization method-based(WSM) solution approach is presented to conduct free vibration analysis of a composite laminated beam with general boundary conditions in this paper.The first-order shear deformation theory considering the shear effect and rotary inertia is used to establish the theoretical model,and weightings are introduced to obtain general boundary conditions.Walsh series are chosen as the basis functions of the meridional directions of the beam,and the integration constants generated in this process are determined by the boundary conditions.By using the WSM,the complex multivariable coupled equations can be transformed into simple linear algebraic equations of a single variable.On this basis,the frequencies of the composite laminated beam can be easily obtained by solving algebraic equations.Compared with the existing literature,the numerical results show that this method has good convergence and accuracy.

关 键 词：Walsh级数法 自由振动 纤维层合梁 

分 类 号：O302[理学—力学]