黏弹性圆弧曲梁在均布随从力作用下的动力分析

基于动力稳定理论的D＇Alembert原理,给出了在时域内同时考虑拉伸黏性和剪切黏性的黏弹性Timoshenko圆弧曲梁在均布随从力作用下的屈曲运动微分方程,并采用归一化幂级数法建立起该非保守系统的复特征方程,根据齐次边界条件,分离出复特征方程的实部和虚部。运用拟牛顿法,研究了两端简支、两端固定和左端简支右端固定3种不同支承黏弹性圆弧曲梁的动力稳定性,并同黏弹性直梁的动力稳定性作了分析比较。

Dynamical Analysis on the Stability of Viscoelastic Circular Beam under the Action of Uniform Accompanied Forces

According to the D＇Alembert principle in dynamic stability theory,this paper establishes the differential equation of curvature movement of Timoshenko viscoelastic circular beam under the action of uniform accompanied forces considering the pulling viscosity and shearing viscosity simultaneously in time domain,and derives the complex eigenvalue equation of the nonconservative system by using the normalized power series method,separates the real part and the imaginary part of the complex eigenvalue equation based on the homogeneous boundary condition,and with the use of quasi-Newton method,researches the dynamic stability of the viscoelastic circular beamunder three different boundary conditions such as simply-simply,clamped-clamped and simply-clamped ends,and makes the comparative analysis on the dynamic stability of the viscoelastic straight beam.