Primary, superharmonic and subharmonic resonances control of an oscillatory cantilever beam excited transversely at its free end

IF 0.9 Q2 MATHEMATICS

Afrika Matematika Pub Date : 2025-04-18 DOI:10.1007/s13370-025-01305-w

Eman Desoky, Magdy Kamel, Ali Kandil

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引用次数: 0

Abstract

The nonlinear vibrations of a cantilever beam model and the dynamic analysis of several resonances (primary and secondary) controlled by the proportional-derivative (PD) control are studied and discussed. The multiple time-scales method is applied to solve the dynamical system of the cantilever beam where the response curves before and after control are obtained. Through these curves, the stability of the beam’s oscillatory behavior is tested under the effect of different physical parameters. The beam suffers from high vibration amplitudes in each resonance case, especially in the superharmonic and subharmonic resonance cases. Besides the nontrivial amplitude of oscillation, a trivial one appears in some secondary resonance cases. Tuning the control gains can lead to acceptable vibration mitigation levels besides approaching the trivial amplitude in some resonance cases. Accordingly, the analytical and numerical results are compared before and after control to validate the control law.

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悬臂梁自由端横向激发的一次谐振、超谐波谐振和次谐波谐振控制

研究和讨论了悬臂梁模型的非线性振动，以及比例导数控制下的几种主共振和次共振的动力学分析。采用多时间尺度方法对悬臂梁的动力系统进行求解，得到了控制前后的响应曲线。通过这些曲线，测试了在不同物理参数影响下梁的振荡行为的稳定性。梁在各种共振情况下，特别是在超谐波和次谐波共振情况下，振动幅值都很高。除了振荡的非平凡振幅外，在某些次共振情况下还出现了一个平凡振幅。在某些共振情况下，除了接近微不足道的振幅外，调整控制增益还可以导致可接受的振动缓解水平。在此基础上，对比了控制前后的解析结果和数值结果，验证了控制律的正确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Afrika Matematika MATHEMATICS-

CiteScore

2.00

自引率

9.10%

发文量