弦-梁耦合系统的动力学行为分析

王霞;李建平

振动与冲击 ›› 2014, Vol. 33 ›› Issue (5) : 53-57.

PDF(1334 KB)
PDF(1334 KB)
振动与冲击 ›› 2014, Vol. 33 ›› Issue (5) : 53-57.
论文

弦-梁耦合系统的动力学行为分析

  • 王霞1,2 李建平2
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Dynamical analysis of a string-beam coupled system

  • WANG Xia1,2, LI Jian-ping2
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摘要

本文研究了弦-梁耦合系统在初始平衡解处的稳定性与分岔情况,给出了特征值随阻尼参数的变化情况,并利用稳定性分析和特征值分析等解析方法,得到了初始平衡解、周期解和拟周期解的稳定边界以及导致Hopf分岔和2维胎面等分岔解的临界分岔曲线。最后,利用数值模拟方法研究了弦-梁耦合系统的稳定性与分岔情况。

Abstract

The stability and bifurcations of a string-beam coupled system at the initial equilibrium solution are investigated with a combination of analytical and numerical methods in detail in this paper. The behavior of the eigenvalues with the parameters is investigated. Based on the averaged equation, the expressions for the critical bifurcation lines leading to incipient and secondary bifurcations, such as Hopf bifurcation and 2-D tori, are obtained. Numerical simulations of these bifurcation cases are also obtained, which agree with the analytical results, at least qualitatively.

关键词

弦-梁耦合系统 / 稳定性 / 分岔 / 周期解

Key words

A string-beam coupled system / Stability / Bifurcation / Periodic solution.

引用本文

导出引用
王霞;李建平. 弦-梁耦合系统的动力学行为分析[J]. 振动与冲击, 2014, 33(5): 53-57
WANG Xia;LI Jian-ping. Dynamical analysis of a string-beam coupled system[J]. Journal of Vibration and Shock, 2014, 33(5): 53-57

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