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

被引：0

作者：

Eman Desoky ^{[1
]}

Magdy Kamel ^{[2
]}

Ali Kandil ^{[2
]}

机构：

[1] Menoufia Higher Institute of Engineering and Technology,Department of Basic Science

[2] Menoufia University,Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering

[3] Egypt-Japan University of Science and Technology (E-JUST),Department of Applied and Computational Mathematics, Institute of Basic and Applied Sciences

来源：

Afrika Matematika | 2025年 / 36卷 / 2期

关键词：

Cantilever beam; Proportional-Derivative controller; Primary resonance; Secondary resonance; Trivial solution; 70G60; 37C75; 37G10; 34C23; 70K50; 70J40; 74K10;

D O I：

10.1007/s13370-025-01305-w

中图分类号：

学科分类号：

摘要：

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.

引用

共 9 条

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