粘弹性地基上损伤弹性Timoshenko梁动力学行为

DYNAMICAL BEHAVIORS OF ELASTIC TIMOSHENKO BEAMS WITH DAMAGE ON VISCOELASTIC FOUNDATION

建立了粘弹性地基上损伤弹性Timoshenko梁在有限变形情况下的运动微分方程,这是一组非线性偏微分方程.为了便于分析,首先利用Galerkin方法对该方程组进行简化,得到一组非线性常微分方程.然后利用Matlab软件进行数值模拟,考察了载荷参数、地基粘性参数和弹性参数、损伤对梁振动的影响.采用非线性动力学中的各种数值方法,如时程曲线、相平面图、Poincare截面和分叉图,发现增大地基的粘弹性参数,有利于增强结构运动的稳定性,而损伤会降低结构运动的稳定性.

The differential equations of motion governing nonlinear dynamical behavior of elastic Timoshenko beams with damage on viscoelastic foundation are given in this paper. It is known that the derived equations are a set of nonlinear partial differential equations. To this end, the Galerkin method is firstly applied to simplify this set of equations, and a set of ordinary differential equations are obtained. The Matlab software is then used to simulate the dynamical behaviors of the elastic Timoshenko beams. Meanwhile, the influence of the load and the viscoelastic parameters of foundation and the damage on the dynamic behaviors of beams is also studied. Various numerical methods of nonlinear dynamics are used including time history curves, phase trajectory diagram, Poincare sections and bifurcation figures. It is found that The stability of movement of the structure is strengthened when the viscoelastic parameters of foundation are increased, but the damage of the Timoshenko beams reduces the stability of movement of the structure.