粘弹性迭层板非线性动力弯曲问题的描述及建模

Formulation and Model of the Problem of Nonlinear Dynamic Bending for Viscoelastic Laminated Plates

假设粘弹性迭层薄板的每一层都是各向同性的线性粘弹体 ,泊松比为常数 ,利用线性粘弹性理论中的Boltzmann叠加原理 ,由非线性几何方程和Karman方程 ,建立了线性粘弹性迭层薄板的非线性动力方程。这是一个二元积分 -非线性偏微分方程组。就粘弹性简支矩形迭层板 ,给出非线性动力初边值问题及方程组 ,并对粘弹性薄板这一特例用迭层板的方法进行了计算 。

In this paper, based on hypothesis that the Poisson ratio is constant, a problem of nonlinear dynamic bending for isotropic linear viscoelastic laminated plates is formulated, and a set of equations for the problem is established through Boltzmann superposition principle in linear viscoelastic theory, nonlinear geometrical equations and Karman equations. The set of the equations for the problem mentioned above is a set of integral-nonlinear partial differential equations with two unknowns. For simple- supported rectangular viscoelastic laminated plates with a periodic load, the initial-value and boundary-value problem of nonlinear dynamic bending is given. For viscoelastic thin plates, the numeric results obtained by that mentioned in this paper are the same as by that only appropriate for thin plates.