基于Kelvin模型的粘弹性浅拱的动力稳定性

研究了外激励作用下非线性粘弹性浅拱的动力行为．通过达朗贝尔原理和欧拉一贝努利假定建立了浅拱的动力学控制方程，其中采用Kelvin模型来表示非线性粘弹性材料的本构关系，并利用Galerkin法将方程简化用于数值分析．分析了粘弹性材料参数、浅拱矢高、外激励幅值和频率对系统分岔和混沌等非线性动力学行为的影响，结果表明各种参数条件下系统的非线性动力特性十分复杂，周期运动、准周期运动和混沌运动窗口在一定条件下交替出现．

The dynamic behaviors of viscoelastic shallow arches based on kelvin modeld

The dynamic of nonlinear viscoelastic shallow arches subjected to the external excitation was investiga- ted. Based on the d＇ Alembert principle and the Euler-Bernoulli assumption, the governing equation of shallow arch was obtained, where the Kelvin model was used to express the constitutive relation of nonlinear viscoelastic material, and the equation was simplified by the Galerkin＇ s method for numerical analysis. Moreover, the effects of the viscoelastic material parameter, the rise and excitation on the nonlinear dynamic including system bifurcation and chaos of shallow arch were investigated viscoelastic shallow arches were very complex, and appeared alternately for certain condition. The results show that the nonlinear dynamic properties of the the periodic motion, quasi-periodic motion and chaotic motion