在有限变形条件下损伤粘弹性梁的动力学行为

本文在有限变形条件下，根据损伤粘弹性材料的一种卷积型本构关系和温克列假设，建立了粘弹性基础上损伤粘弹性Timoshenko梁的控制方程。这是一组非线性积分——偏微分方程。为了便于分析，首先利用Galerkin方法对该方程组进行简化，得到一组非线性积分一常微分方程。然后应用非线性动力学中的数值方法，分析了粘弹性地基上损伤粘弹性Timoshenko梁的非线性动力学行为，得到了简化系统的相平面图、Poincare截面和分叉图等。考察了材料参数和载荷参数等对梁的动力学行为的影响。特别，考察了基础和损伤对粘弹性梁的动力学行为的影响。

Dynamical Behaviors of Visco-elastic Beams with Damage under Finite Deformation

From a convolution type constitutive model of viscoelastic solids with voids and Winkler assumption, the governing equations of the static-dynamic analysis of viscoelastic Timoshenko beams with damage were presented under the case of finite deflections. It can see that the derived equations are a set of nonlinear integro-partial-differential equations. In order to analyze, the Galerkin method was firstly applied to simplify the set of equations and a set of ordinary-differential equations were obtained. The numerical methods in nonlinear dynamics were used to solve the simplified systems. Phase-trajectory figures and bifurcation figures were all obtained. It can be seen that there are plenty of dynamic properties for nonlinear dynamical systems formed by this kind of viscoelastic Timoshenko beams under finite deflections. The influences of the material and load parameters on the dynamical behavior of beams were investigated in detail. In special, the effects of the foundation and damage on the dynamical behaviors of viscoelastic Timoshenko beams were considered.