点弹性支承下非保守粘弹性杆的稳定性分析

Stability Analysis of Viscoelastic Rod with Elastic Point Supports Subjected to NonConservative Forces

用积分方程法研究了具有多个点弹性支承的Kelvin型粘弹性简支杆在切向均布随从力作用下的动力特性和稳定性问题。对该微分方程的复特征值问题,先用叠加原理求核函数,将微分方程化为积分方程;再利用退化核特性,从积分方程导出复特征方程;算例分析了点弹性支承的弹性系数、支承位置和材料的无量纲延滞时间对杆的自振频率和稳定性的影响。结果表明,该方法能有效地处理广义δ函数及变系数的微分方程的复特征值问题。

The dynamic behaviors and stability of Kelvin's viscoelastic rods with interior elastic point supports subjected to uniformly distributed tangential follower forces are investigated by integral equation theory. In solving the complex characteristic problem of the differential equation,the nucleus function is first obtained by using superposition principle, and the differential equation of vibrator mode is reduced to an integral equation. Then, based on the integral equation, complex characteristic equation is derived in accidence with the properties of degenerative nucleus. At last, the effect of the elastic constant of the elastic point supports, location of point support and dimensionless delay time of Kelvin's materials on selfvibration complex frequencies and stability of nonconservative rods are analyzed by the examples. The calculated examples indicate that the proposed method is effective and practical in solving the complex eigenvalue problem of differential equation with generalizedfunction and complex variable coefficients.