超临界轴向运动Timoshenko梁横向受迫振动

Transverse forced vibration of an axially moving Timoshenko beam at a supercritical speed

研究外部激励作用下,超临界轴向运动Timoshenko梁横向非线性振动的稳态响应。通过对非零平衡位形的坐标变换,从轴向运动Timoshenko梁的横向振动控制方程推导得到超临界速度下受横向外部激励的陀螺系统标准控制方程。运用Galerkin截断法数值研究超临界下轴向运动Timoshenko梁的稳态周期幅频响应关系,并通过与超临界速度下轴向运动Euler-Bernoulli梁的稳态幅频响应曲线进行对比,研究Euler-Bernoulli梁理论的适用范围。

In this paper,the transverse nonlinear forced vibration of an axially moving Timoshenko beam at a supercritical speed was studied under external excitation. In the supercritical region,the standard control equation of the gyro system,under the lateral external incentives,was derived based on the governing equation of transverse nonlinear vibration of the axially moving Timoshenko beam. Moreover,the steady-state amplitude frequency response relationship of the axially moving Timoshenko beam at a supercritical speed was investigated by using the Galerkin method. Furthermore,the effects of system parameters on the steady-state amplitude frequency response relationship of the Timoshenko beam were considered. Comparisons with Euler-Bernoulli（ E-B） beam reveal that the resonance frequency of the Timoshenko beam is much lower and the resonance amplitude is higher in the supercritical region.