粘弹性Timoshenko梁的变分原理和静动力学行为分析

从线性，各向同性，均匀粘弹性材料的Boltzmann本构定律出发，通过Laplace变换及其反变换，由三维积分型本构关系给出了Timoshenko梁的本构关系，并由此建立了小挠度情况下粘弹性Timoshenko梁的静动力学行为分析的数学模型，一个积分－偏微分方程组的初边值问题。同时，采用卷积，建立了相应的简化Gurtin型变分原理。给出了两个算例，考查了梁的厚度h与梁的长度l之比β对梁的力学行为的影响。

VARIATIONAL PRINCIPLE AND STATIC-DYNAMIC ANALYSIS FOR VISCOELASTIC TIMOSHENKO BEAMS

The Boltnmann superposition principle of linear, isotropic and viscoelastic materials are applied to analyze static dynamic behaviors of viscoelastic Timoshenko beam. Under the condition of small deflections, the initial boundary value problem for analyzing static dynamic behaviors of homogeneous, isotropic, viscoelastic Timoshenko beams is formulated by using Laplace transformation and its inverse transformation. They are a set of linear integro partial differential equations. At the same time, the corresponding variational principle on static dynamic analysis of viscoelastic Timoshenko beams subjected to both transverse and axial loads are proposed. The exact solution for the quasi static problem of a simply supported viscoelastic Timoshenko beams is given from the elastic viscoelastic correspondence principle. The dynamic behaviors of viscoelastic Timoshenko beam under two kinds of loads are studied by using Galerkin method and the effect of transverse shear is considered.