›› 2012, Vol. 32 ›› Issue (3): 25-28.DOI: 10.3969/j.issn.1006-1355.2012.03.006

• 2.振动理论与数值解法 • Previous Articles     Next Articles

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

SHAO Wen-yun 1, ZHANG Guo-ce 2, WANG Zhi-feng 3   

  1. ( 1. School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072, China;2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; 3. Shanghai Posts & Telecommunications Designing Consulting Institute Co., Ltd, Shanghai 200092, China )
  • Received:2011-07-13 Revised:2011-08-10 Online:2012-06-18 Published:2012-06-18
  • Contact: Guo-Ce ZHANG

高速轴向运动梁横向受迫振动的稳态分析

邵文韫1,张国策1,王志锋2   

  1. ( 1. 上海大学 机电工程与自动化学院, 上海 200072；2. 上海大学 上海市应用数学和力学研究所, 上海 200072；3. 上海邮电设计咨询研究院有限公司， 上海 200092 )
  • 通讯作者: 张国策

Abstract: 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.

Key words: vibration and wave, high-speed axially moving beam, nonlinearity, forced vibration, steady-state response, Galerkin method

摘要： 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。

关键词: 振动与波, 高速轴向运动梁, 非线性, 受迫振动, 稳态响应, Galerkin方法

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