粘弹性正交各向异性对称层合板的非线性动力响应

Nonlinear Dynamic Responses of Viscoelastic Orthotropy Symmetric Laminated Plates

分析了几何非线性粘弹性正交各向异性对称层合矩形板的非线性动力响应问题.由Kirchhoff假设,Boltzmann算子和Karman方程,在假设poisson比为常数的条件下,推导了粘弹性正交各向异性对称层合板的非线性动力方程,该方程为一非线性偏微分 积分方程组.经无量纲化和应用Galerkin方法之后,得到关于时间变量的非线性微分 积分型的方程,以三层(单层各向同性)对称矩形层合板作为特例进行数值计算,得到不同材料性质对频谱曲线以及时间 位移曲线的影响,当退化为各向同性粘弹性薄板时,其计算结果与文[1]的一致.

On the basis of the Kirchhoff hypothesis, the Boltzmann operator and the Karman theory, and assuming that Poisson ratio is constant, the nonlinear dynamic equations of viscoelastic orthotropy symmetric laminated plates are derived. The equations are a set of nonlinear partial differentialintegral equations. By using dimensionless parameters and the Garlerkin method, a set of nonlinear ordinary differentialintegral equations about time variables is obtained. For a symmetric ply plate(each layer is isotropic) with three layers, some of computational results are presented. The different frequencyspectrum and timedeflection curves for different materials are obtained. The numeric results are compared with the data in Ref. and a good agreement is made when the symmetric laminated plates degenerate into viscoelastic thin plates.