工程力学 ›› 2019, Vol. 36 ›› Issue (12): 15-23.doi: 10.6052/j.issn.1000-4750.2019.01.0021

• 基本方法 • 上一篇    下一篇

随从力作用轴向运动叠层板的亚谐波共振

张晓宇1,2, 胡宇达1,2   

  1. 1. 燕山大学建筑工程与力学学院, 河北, 秦皇岛 066004;
    2. 燕山大学河北省重型装备与大型结构力学可靠性重点实验室, 河北, 秦皇岛 066004
  • 收稿日期:2019-01-17 修回日期:2019-08-14 出版日期:2019-12-25 发布日期:2019-09-29
  • 通讯作者: 胡宇达(1968-),男,黑龙江人,教授,博士,博导,主要从事非线性动力学、电磁弹性力学研究(E-mail:huyuda03@163.com). E-mail:huyuda03@163.com
  • 作者简介:张晓宇(1994-),女,内蒙古人,硕士生,主要从事非线性动力学研究(E-mail:zhangxiaoyu_0501@163.com).
  • 基金资助:
    国家自然科学基金项目(11472239)

SUBHARMONIC RESONANCE OF AXIALLY MOVING LAMINATEED PLATES SUBJECTED TO FOLLOWER FORCES

ZHANG Xiao-yu1,2, HU Yu-da1,2   

  1. 1. School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, Hebei 066004, China;
    2. Hebei Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures, Yanshan University, Qinhuangdao, Hebei 066004, China
  • Received:2019-01-17 Revised:2019-08-14 Online:2019-12-25 Published:2019-09-29

摘要: 研究随从力作用轴向运动正交各向异性叠层板的亚谐波共振问题。基于给出的叠层板动能、势能、中面应变势能、轴向拉力引起的应变势能以及外力虚功,通过哈密顿原理导出叠层板的非线性振动方程。将非线性振动方程运用伽辽金积分法离散并进行无量纲化,推得关于时间变量的非线性振动微分方程组。应用多尺度法求解非线性方程组,分别得到前三阶模态稳态运动下1/3亚谐波共振幅频响应方程。最后通过算例分析,得到了振幅-调谐值特性变化曲线图、振幅-速度特性变化曲线图、振幅-激励幅值特性变化曲线图和激发共振双值解临界点曲线图。结果表明,共振幅值均是双值解,不同阶共振振幅有明显区别。

关键词: 叠层板, 轴向运动, 亚谐波共振, 随从力, 多尺度法

Abstract: The subharmonic resonance of the axially moving orthotropic laminated plates under follower force was investigated. Based on the kinetic energy, potential energy, mid-plane strain potential energy, the strain potential energy caused by the axial tensile force and the external virtual work, the nonlinear vibration equations of the laminated plate were derived by using the Hamiltonian principle. The dimensionless nonlinear vibration differential equations with regards to time were achieved by using the Galerkin method. The multi-scale method was used to solve differential equations of the 1/3 subharmonic resonance, and the amplitude-frequency response equations of steady-state motion for different modes were obtained. Finally, through the analysis of the examples, the characteristic curves of amplitude varying with different parameters, e.g., the tuning parameter, the velocity, the excitation amplitude, and the critical point curves for exciting double-value resonance were plotted, respectively. The results showed that the resonance amplitudes were double-valued. Moreover, the amplitudes in different modal resonance cases were obviously different.

Key words: laminates, axial motion, subharmonic resonance, follower forces, multiple scales method

中图分类号: 

  • O322
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