Position and Velocity Time Delay for Suppression Vibrations of a Hybrid Rayleigh-Van der Pol-Duffing Oscillator

被引：8
作者：
Amer, Y. A. [1 ]
El-Sayed, A. T. [2 ]
Abd El-Salam, M. N. [3 ]
机构：
[1] Zagazig Univ, Sci Fac, Math Dept, Zagazig, Egypt
[2] Modern Acad Engn & Technol, Basic Sci Dept, Cairo, Egypt
[3] Higher Technol Inst, Basic Sci Dept, 10th Of Ramadan City, Egypt
来源：
SOUND AND VIBRATION | 2020年 / 54卷 / 03期
关键词：
Position time delay feedback; velocity time delay feedback; multiple scales method; resonance cases; BIFURCATION; CONTROLLER; SYSTEM;
D O I：
10.32604/sv.2020.08469
中图分类号：
O42 [声学];
学科分类号：
070206 ; 082403 ;
摘要：
In this paper, we used time delay feedback to minimize the vibrations of a hybrid Rayleigh-van der Pol-Duffing oscillator. This system is a one-degree-of-freedom containing the cubic and fifth nonlinear terms and an external force. We applied the multiple scales method to get the solution from first approximation. Graphically and numerically, we studied the system before and after adding time delay feedback at the primary resonance case (Omega congruent to omega). We used MATLAB program to simulate the efficacy of different parameters and the time delay on the main system.
引用
收藏
页码：149 / 161
页数：13
相关论文
共 23 条
[1]   Effects of time delay on an active vibration control of a forced and Self-excited nonlinear beam [J].
Abdelhafez, Hassan ;
Nassar, Mohamed .
NONLINEAR DYNAMICS, 2016, 86 (01) :137-151
[2]   Nonlinear vibration and of the Duffing oscillator to parametric excitation with time delay feedback [J].
Amer, Y. A. ;
EL-Sayed, A. T. ;
Kotb, A. A. .
NONLINEAR DYNAMICS, 2016, 85 (04) :2497-2505
[3]  
AMER YA, 2015, SCI RES ESSAYS, V10, P489, DOI DOI 10.5897/SRE2015.6208
[4]  
Barron Miguel Angel, 2016, J. appl. res. technol, V14, P62, DOI 10.1016/j.jart.2016.01.002
[5]   Periodic solution of the generalized Rayleigh equation [J].
Cveticanin, L. ;
El-Latif, G. M. Abd ;
El-Naggar, A. M. ;
Ismail, G. M. .
JOURNAL OF SOUND AND VIBRATION, 2008, 318 (03) :580-591
[6]   Effects of delayed time active controller on the vibration of a nonlinear magnetic levitation system to multi excitations [J].
El-Ganaini, Wedad A. ;
Kandil, Ali ;
Eissa, Mustafa ;
Kamel, Magdy .
JOURNAL OF VIBRATION AND CONTROL, 2016, 22 (05) :1257-1275
[7]   Vibration control of helicopter blade flapping via time-delay absorber [J].
El-Sayed, A. T. ;
Bauomy, H. S. .
MECCANICA, 2014, 49 (03) :587-600
[8]  
Guckenheimer J., 1984, Journal of Applied Mechanics, V51, P947, DOI DOI 10.1115/1.3167759
[9]   Multiple scales scheme for bifurcation in a delayed extended van der Pol oscillator [J].
Huang, Chengdai .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2018, 490 :643-652
[10]   Analytical solution for Van der Pol-Duffing oscillators [J].
Kimiaeifar, A. ;
Saidi, A. R. ;
Bagheri, G. H. ;
Rahimpour, M. ;
Domairry, D. G. .
CHAOS SOLITONS & FRACTALS, 2009, 42 (05) :2660-2666
123