力学与实践 ›› 2022, Vol. 44 ›› Issue (4): 890-894.DOI: 10.6052/1000-0879-21-513

• 应用研究 • 上一篇    下一篇

含阻尼效应的黏弹性杆稳态响应的解析解

陈波, 李映辉(), 李翔宇, 袁江宏   

  1. 西南交通大学力学与航空航天学院,成都 610031
  • 收稿日期:2021-11-19 出版日期:2022-08-08 发布日期:2022-08-17
  • 作者简介:李映辉,教授,研究方向为结构振动与控制、工程结构数值仿真和结构非线性动力学等。E-mail: yhli2007@sina.com
  • 基金资助:
    国家自然科学基金(11872319)和西南交通大学2021年本科教育教学研究与改革项目(2103107)资助。

ANALYTICAL SOLUTIONS OF STEADY-STATE RESPONSES OF A VISCOELASTIC ROD WITH THE DAMPING EFFECT

CHEN Bo, LI Yinghui(), LI Xiangyu, YUAN Jianghong   

  1. School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, China
  • Received:2021-11-19 Online:2022-08-08 Published:2022-08-17

摘要:

基于格林函数法和叠加原理,给出了简谐激励下开尔文黏弹性杆稳态响应的解析解。运用拉普拉斯变换法得到了任意边界条件下黏弹性杆强迫振动的格林函数解。设计了一个统一方案,将杆的各种边界表示为矩阵形式,便于确定格林函数中的待定常数。算例表明,材料黏性阻尼和外部阻尼导致杆位移在空间和时间上不可分离。

关键词: 黏弹性杆, 外部阻尼, 稳态响应, 格林函数法, 任意边界条件

Abstract:

In this paper, the analytical solutions of the steady-state responses of a viscoelastic rod in Kelvin’s model subjected to time-harmonic forces are derived based on Green’s function method and the superposition principle. Laplace transform method is employed to obtain Green’s function for the forced vibration of the viscoelastic rod with arbitrary boundary conditions. A unified strategy applied to various boundaries is proposed to determine unknown constants involved in the Green’s function. Computational results show that the dynamic deflection of the rod considering viscous damping of the material and external damping is not separable in time and space.

Key words: viscoelastic rod, external damping, steady-state responses, Green's function method, arbitrary boundary conditions

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