材料和几何非线性粘弹性柱的动力学模型及其简化

A dynamical model viscoelastic columns with material and geometric nonlinearities and its simplification

建立了描述具有几何和物理非线性均匀柱动力学行为的偏微分—积分方程 ,柱的材料满足Leadder man非线性本构关系 .对于两端简支的情形 ,采用Galerkin方法简化为常微分—积分方程 ;

The integro partial differential equation that governs the dynamical behavior of homogeneous viscoelastic columns with material and geometric nonlinearities is established The material of the columns obeys the Leaderman nonlinear constitutive relation.In the case of two simple supported ends,the Galerkin method is applied to simplify the equation to a integro differential equation.The equation is further simplified to a set of differential equations by introducing an additional variable.