粘弹性板的非线性动力稳定特性分析

采用Boltzman积分型本构关系,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,发现粘弹性结构具有与一般阻尼系统不同的动力稳定特性,由于材料的粘性阻尼与松弛效应的综合影响,动力不稳定区域有不同程度的缩小与偏移,且在考虑几何线性与非线性情形下,其影响程度又不一样.

FEATURES OF THE NONLINEAR DYNAMIC STABILITY FOR VISCOELASTIC PLATES

The dynamic stability of viscoelastic thin plates is investigated with linear kinematics and nonlinear kinematics. The Boltzman's hereditary constitutive relationship is used to model the rectangular plates hinged on four sides 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 the first unstable region on the diagram of frequency ratio and amplitude of in plane excitation. Some different features from general elastic systems with damping are discovered.It shows that the first unstable region will not only contract but also downwards deviate as compared with the elastic results, and the factor of nonlinear kinematics will strengthen the feature of downward deviation.