高速轴向运动梁横向受迫振动的稳态分析

在两端简支边界条件下，研究超临界速度范围内轴向运动梁横向非线性受迫振动的稳态响应。考虑Kelvin本构关系，通过坐标变换建立一个积分偏微分方程，以此描述高速轴向运动梁受到一个周期的外激励后所作的微幅振动。用8阶Galerkin方法截断标准控制方程，然后使用有限差分法计算受迫振动稳定的稳态响应。结果表明，在超临界速度范围，当激励频率接近前两阶固有频率时存在共振现象。

Steady-state Analysis of Forced Transverse Vibration for an Axially Moving Beam at High-speed

The steady-state periodic response of transversely forced vibration of a simply supported viscoelastic beam moving axially at the supercritical speed was investigated. It was assumed that the external excitation is spatially uniform and temporally harmonic. Based on the coordinate transform, a nonlinear integro-partial-differential equation governing the small transverse vibration of the beam was constituted by the Kelvin model. The first two resonances were analyzed via the 8-term Galerkin truncation method. Based on the Galerkin truncation, the finite difference schemes were developed to compute the stable steady-state response. Numerical simulations display that the resonance occurs if the load frequency approaches any natural frequency in the supercritical speed range.