任意直四边形复合材料层合板振动特性研究

Vibration characteristics of arbitrary straight quadrilateral composite laminates

为研究任意直四边形板的振动机理,本文基于一阶剪切变形理论推导任意直四边形复合材料层合板的振动控制方程和一般弹性边界方程,并采用无网格法对方程进行离散化处理得到结构的振动特征方程,同时结合移动最小二乘法对离散化的振动特征方程进行求解。在验证了所建模型的正确性和收敛性的前提下,研究了材料杨氏模量比、结构边界条件、结构纤维铺设方式与铺设层数对层合板振动特性的影响。研究表明:本方法能有效预测任意直四边形层合板的振动特性。纤维铺设方式为[θ,-θ]时,随着铺设角度θ的变化,板的无量纲固有频率有关于θ=90°对称的现象,其余铺设方式则没有对称性。板的无量纲固有频率随着铺设层数的增加呈锯齿状增加的趋势。

To study the vibration mechanism of arbitrary straight quadrilateral plates,in this paper,the vibration governing equations and general elastic boundary equations of arbitrary straight quadrilateral composite laminates are derived based on the first-order shear deformation theory.The meshless method is used to discretize the equation to obtain the vibration characteristic equation of the structure and,simultaneously,solve the discretized vibration characteristic equation with the moving least square method.Under the premise of verifying the correctness and convergence of the built model,the effects of the material Young′s modulus ratio,structural boundary conditions,structural fiber laying methods,and number of laying layers on the vibration characteristics of laminates are studied.The research results show that this method can effectively predict the vibration characteristics of any straight quadrilateral laminate.When the fiber laying form is[θ,-θ],as the laying angleθchanges,the dimensionless natural frequency of the board is symmetrical with respect toθ=90°,whereas the other laying methods have no symmetry.The dimensionless natural frequency of the board tends to increase in a zigzag manner with the increase in the number of laying layers.