粘弹性曲梁的动力稳定性

利用线性粘弹性力学中的微分型本构关系,建立了粘弹性Timoshenko曲梁在均布随从力作用下的屈曲运动微分方程。分离屈曲位移中的空间变量和时间变量,采用归一化幂级数法建立起该非保守系统的复特征方程,在考察位移单值性条件的基础上,运用拟牛顿法得出粘弹性曲梁振动参数随随从力的变化关系曲线,研究了支承条件对粘弹性曲梁非线性动力稳定性的影响,并考察了材料粘性对结构动力稳定性的影响。

Dynamic Stability of Viscoelastic Curved Beam Under Following Forces

Using differential constitutive relation for the linear viscoelastic mechanics,the inflective differential equation of the viscoelastic Timoshenko curved beam accompanying following forces has been established.Spatial variables were separated from time variable in inflective displacement.Normalized power series method was adopted to establish the complex characteristic equation of the conservative system.On the base of uniqueness of the displacement value,the quasi-Newton method was adopted to obtain the curve relating vibration parameter and the following force for the viscoelastic curved beam.The impacts of supporting condition and material viscosity over the nonlinear dynamic stability of the viscoelastic curved beam have also been studied.