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Nonlinear modes of piecewise linear systems forced vibrations close to superharmonic resonances
Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering ( IF 2.4 ) Pub Date : 2019-08-29 , DOI: 10.1177/0954406219869967
B Uspensky 1 , K Avramov 1 , O Nikonov 2
Affiliation  

Superharmonic resonances of the periodic vibrations are observed in many nonlinear dynamical systems. The multiple scales method is used to analyze the superharmonic forced vibrations of nonlinear systems in asymptotic limit.1 The superharmonic resonances of the circular plate forced vibrations are analyzed by Srirangarajan.2 The longitudinal-transverse superharmonic shaft vibrations are described by the system of the ordinary differential equations with small parameter in Zou et al.3 The multiple scales method is used to analyze these resonance vibrations. The effect of the non-linear magnetic forces on the non-linear response of the shaft is examined for the case of the superharmonic resonance by multiple scales method in Ji and Leung.4 It is shown that the periodic superharmonic motions undergo the saddle-node and the Hopf bifurcations. The third-order superharmonic resonance in the harmonically excited Duffing oscillator is analyzed by Hassan.5 The recurrent bifurcation behavior of the superharmonic vibrations is treated in Parlitz and Lauterborn and Parlitz.6,7

中文翻译:

分段线性系统的非线性模式强迫振动接近超谐共振

在许多非线性动力学系统中都观察到周期性振动的超谐共振。采用多尺度方法分析了渐近极限下非线性系统的超谐强迫振动。1 Srirangarajan分析了圆板强迫振动的超谐共振。2 Zou等人的小参数常微分方程组描述了纵向横向超谐轴振动。3多尺度方法用于分析这些共振。在Ji and Leung中,通过多尺度方法研究了超谐波共振情况下非线性磁力对轴非线性响应的影响。4结果表明,周期超谐运动经历了鞍节点和霍普夫分支。哈桑分析了谐波激发的Duffing振荡器中的三阶超谐谐振。5在Parlitz和Lauterborn和Parlitz中处理了超谐波振动的反复分叉行为。6,7
更新日期:2020-01-04
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