Experiment and theory on the nonlinear vibration of a shallow arch under harmonic excitation at the end

被引:30
作者
Chen, Jen-San [1 ]
Yang, Cheng-Han [1 ]
机构
[1] Natl Taiwan Univ, Dept Engn Mech, Taipei 10617, Taiwan
来源
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME | 2007年 / 74卷 / 06期
关键词
D O I
10.1115/1.2165231
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
In this paper we study, both theoretically and experimentally, the nonlinear vibration of a shallow arch with one end attached to an electro-mechanical shaker In the experiment we generate harmonic magneticforce on the central core of the shaker by controlling the electric current flowing into the shaker The end motion of the arch is in general not harmonic, especially when the amplitude of lateral vibration is large. In the case when the excitation frequency is close to the nth natural frequency of the arch, we found that geometrical imperfection is the key for the nth mode to be excited. Analytical formilla relating the amplitude of the steady state response and the geometrical imperfection can be derived via a multiple scale analysis. In the case when the excitation frequency is close to two times of the nth natural frequency two stable steady state responses can exist simultaneously. As a consequence jump phenomenon is observed when the excitation frequency sweeps upward. The effect of geometrical imperfection on the steady state response is minimal in this case. The multiple scale analysis not only predicts the amplitudes and phases of both the stable and unstable solutions, but also predicts analytically the frequency at which jump phenomenon occurs.
引用
收藏
页码:1061 / 1070
页数:10
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