损伤粘弹性厚板的基本动力学方程

Dynamical Equation for Thick Viscoelastic Plate with Voids

该文从粘弹性损伤的基本方程出发,采用带损伤的粘弹性积分型本构关系,利用推导弹性厚板方程相类似的方法,推导了带损伤粘弹性厚板含剪切、挤压及转动惯性效应的动力学方程.它是损伤弹性薄板动力学方程的推广.因此,当不考虑剪切、挤压和转动惯性效应时,此方程还可退化得到粘弹性损伤薄板的动力学方程.

Based on the constitutive equations and integral-type constitutive model of viscoelastic solids, with damage motion differential equations are presented for a general thick viscoelastic plate with damage, including effects of shear deformation, extrusion deformation and rotatory inertia. The derivation is similar to that for the equations of thick elastic plates. These equations are generalization of motion differential equations for the corresponding viscoelastic thin plate with damage. Ignoring shear deformation, extrusion deformation and rotatory inertia, they can be degenerated into motion differential equations for viscoelastic thin plate with damage.