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.