初始应力作用下的横向各向同性梁

Transversely Isotropic Beam under Enitial Stress

本文从Novozhilov的非线性弹性理论基本方程出发,经适当的简化,用沿梁横截面积分的方法导出任意非均匀初始应力场作用下的横向各向同性梁的运动方程.当初始应力不存在时,方程退化为经典的Timoshenk。梁方程,作为例子,本文用所得的方程,研究了在初始轴向力、初始弯矩作用下的横向各向同性梁的屈曲及振动特性。

Starting from Novozhilov's nonlinear equations of elasticity by appropriate simplification and integration over the beam cross section, a linearized set of equations for a transversely isotropic beam under initial non-uniform state of stress is obtained. In the absence of initial stress, the obtained equations are reduced to well-known Timoshenko beam equations. These equations are applied to investigate the vibration and buckling characteristics of a transversely isotropic beam under uniform initial axial force and bending moment