弹性约束边界条件下复合材料层合梁振动特性研究

Vibration Analysis of Laminated Composite Beams with Elastic Boundary Conditions

在一阶剪切变形理论和哈密顿原理的基础上,利用Haar小波离散方法,提出了一种简单、有效的评估一般弹性边界条件下复合材料层合梁振动特性的分析模型。结构位移变量及其相关导数的基函数分别采用Haar小波及其积分表示。在此基础上,利用边界条件求出积分过程中的常数,进而将层合梁的运动方程和边界条件进一步转化为一组线性代数方程。通过求解该线性代数方程,可得到复合材料层合梁的自由振动特性。通过数值算例对比验证了本文模型的正确性。此外,给出了复合材料层合梁的一些新的计算结果,可作为基准解为后续数值方法或解析法提供对比数据。

A simple and efficient method is proposed to evaluate the vibration behavior of the laminated composite beams under elastic boundary conditions with Haar wavelet discretization method,in terms of the first order shear deformation theory and the Hamilton principle.The basis functions for the displacement variables and their derivatives are expressed in terms of Haar wavelet and their integral,respectively.On the basis,the boundary conditions are used to obtain the constants in the integration process,and then the equations of motion and the boundary conditions of the laminated beams are further converted into a group of linear algebraic equations.The natural frequencies of laminated composite beams are obtained by solving the algebraic equations.The correctness and efficiency of the present method is verified by a series of numerical examples.Some new results for the laminated composite beams are presented,which may serve as benchmark solutions.