受轴向激励弹性支承梁的稳定性分析
作者:
作者单位:

作者简介:

通讯作者:

中图分类号:

基金项目:

国家自然科学基金杰出青年项目(12025204)


STABILITY ANALYSIS OF AXIALLY EXCITED BEAM WITH ELASTIC BOUNDARY
Author:
Affiliation:

Fund Project:

  • 摘要
  • |
  • 图/表
  • |
  • 访问统计
  • |
  • 参考文献
  • |
  • 相似文献
  • |
  • 引证文献
  • |
  • 资源附件
  • |
  • 文章评论
    摘要:

    对于广泛存在的弹性支撑梁,首次呈现支承弹簧刚度对轴向激励下梁横向振动稳定性的影响.应用Hamilton原理,建立了两端由线性弹簧支撑的受轴向激励梁的动力学控制方程.通过解析方法计算了受轴向压力梁的固有频率,得到了支撑弹簧刚度与系统固有频率和临界轴力的关系.Galerkin截断后,通过多尺度法和Runge-Kutta法,计算得到了梁参激振动稳态响应的半解析与数值解.讨论了激励幅值、支撑弹簧刚度、平均轴力对系统非线性响应幅值及软硬特性的影响.利用Routh-Hurwitz稳定性判据,求得系统的参激稳定边界,着重讨论了支撑弹簧刚度、阻尼系数的影响.研究发现,边界支撑弹簧的刚度可以显著改变受轴向激励梁的参激稳定边界.因此,研究结果将为广泛存在受到轴向激励结构的设计提供指导.

    Abstract:

    For beams with elastic supports, influence of the spring stiffness on parametric stability boundary of an axially excited beam is presented for the first time. Here, based on Hamilton , s principle, dynamic governing equation of the axially excited beam supported by linear springs on both sides is established. The natural frequen?cies of the beam with axial compression are calculated by the analytical method. The relationships between the stiffness of the supporting spring, the natural frequencies and the critical loading of the system are obtained. Based on Galerkin truncation, semi-analytical and numerical solutions of the steady-state response are obtained by the multi-scale method and the Runge-Kutta method. The effects of the excitation amplitude, supporting stiffness and the average axial force on the nonlinear response are discussed. The stability boundary of the parametric resonance is obtained by the Routh-Hurwitz stability criterion. The influence of the supporting stiffness and the damping on the stability of the parametric resonance are fully discussed. It is found that the stiffness of the supporting spring can significantly change the parametric stability boundary of the beam. Therefore, the results will provide guidelines for design of structures subjected to axial excitation.

    参考文献
    相似文献
    引证文献
引用本文

张弛,毛晓晔,丁虎,陈立群.受轴向激励弹性支承梁的稳定性分析[J].动力学与控制学报,2022,20(3):66~76; Zhang Chi, Mao Xiaoye, Ding Hu, Chen Liqun. STABILITY ANALYSIS OF AXIALLY EXCITED BEAM WITH ELASTIC BOUNDARY[J]. Journal of Dynamics and Control,2022,20(3):66-76.

复制
分享
文章指标
  • 点击次数:
  • 下载次数:
  • HTML阅读次数:
  • 引用次数:
历史
  • 收稿日期:2021-04-14
  • 最后修改日期:2021-05-04
  • 录用日期:
  • 在线发布日期: 2022-06-30
  • 出版日期:

微信公众号二维码

手机版网站二维码