湿热环境下粘弹性板的非线性动力稳定性分析

The Analysis of Nonlinear Dynamic Stability for Viscoelastic Plates in Hygrothermal Environment

采用Boltzman积分型本构关系和热流变简单材料的折减时间概念,考虑湿热环境对材料粘弹性动力学行为的影响,分析了线粘弹性薄板在考虑几何线性与非线性时的长期动力稳定特性.设材料为标准线性固体,将系统的微分-积分型控制方程转化成微分型控制方程,由增量谐波平衡法确定主要动力不稳定区域的边界。

This paper concerns the dynamic stability of viscoelastic thin rectangular plates in hygrothermal environment with considering geometrically non-linear kinematics. The Boltzman's hereditary constitutive relationship and the concept of reduced time are used to model the plates hinged on four edges and subjected to in-plane period excitation at two opposite sides. The dynamic governing equations with differential-integral type are converted to ones of higher order differential type while the material is characterized as standard linear solids, and the IHB method is applied to determine the boundary of principle unstable region on the diagram of frequency ratio and amplitude of excitation. It turns out that the increasing of temperature and humidity makes the principle unstable region not only contract but also deviate downwards .At the end of the paper, a qualitative explanation is made referring to the effect of shift factors induced by the change of temperature and humidity.