几何非线性的损伤粘弹性Timoshenko梁的动力学行为

DYNAMICAL BEHAVIORS OF NONLINEAR VISCOELASTIC TIMOSHENKO BEAMS WITH DAMAGE

从考虑损伤的粘弹性材料的一种卷积型本构关系出发,建立了在有限变形下损伤粘弹性Timoshenko 梁的控制方程.利用Galerkin方法对该组方程进行简化,得到一组非线性积分-常微分方程.然后应用非线性动力学数值分析方法,如相平面图,Poincare截面分析了载荷参数对非线性损伤粘弹性Timoshenko梁动力学性能的影响.特别考察了损伤对粘弹性梁的动力学行为的影响.

From a convolution type constitutive model of viscoelastic solids with damage, this paper established the equations governing the static-dynamic behaviors of viscoelastic Timoshenko beams with damage under finite deflections. The Galerkin method was applied to simplify the equations, and then a set of ordinarydifferential equations was obtained. The numerical methods, such as Phase-trajectory figures and Poincare sections, were used to solve the simplified system. This paper also investigated the influences of the load parameters on the dynamic behavior of nonlinear viscoelastic Timoshenko beams with damage. In particular, the effects of the damage on the dynamical behaviors of viscoelastic Timoshenko beams were considered.