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.%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追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.
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