Nonlinear Dynamics of a Controlled Cantilever Beam with Varying Orientation under Primary Resonance

Usama H. Hegazy^1,

¹Department of Mathematics, Faculty of Science, Al-Azhar University, P.O. Box 1277, Gaza, Palestine

Cite this paper:
Usama H. Hegazy. Nonlinear Dynamics of a Controlled Cantilever Beam with Varying Orientation under Primary Resonance. American Journal of Mechanical Engineering. 2014; 2(7):316-327. doi: 10.12691/ajme-2-7-31

Abstract

The problem of controlling the oscillations and chaotic behavior of a nonlinear cantilever beam with varying orientation under mixed excitations is tackled. Numerical integration of the second order nonlinear ordinary differential equation is performed with different control strategies to explore the chaotic dynamics of the first mode of the beam at the primary resonance case. The method of multiple scales perturbation technique is applied to obtain approximate solution and the stability of the response is studied. The effects of the various parameters are investigated by numerical simulations.

Keywords:
linear position feedback negative velocity feedback orientation angle

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	M. Yaman, and S. Sen, 2004, The analysis of the orientation effect of the non-linear flexible systems on performance of the pendulum absorber. Inter J Non-linear Mech. 39, 741-752.
[2]	M. Yaman, and S. Sen, 2007, Vibration control of a cantilever beam of varying orientation. Inter J Solids Struct. 44, 1210-1220.
[3]	U. H. Hegazy, 2009. Single-mode response and control of a hinged-hinged flexible beam. Arch Appl Mech, 79, 335-345.
[4]	A. F. El-Bassiouny, 2005. Single-mode control and chaos of cantilever beam under primary and principal parametric excitations. Chaos, Sol. Fract., 30(5), 1098-1121.
[5]	M. Eissa, N. A. Saeed, and W. A. El-Ganini, 2013. Saturation-based active controller for vibration suppression of a four-degree-of-freedom rotor AMB system, Nonlinear Dyn., 76(1), 743-764.
[6]	W. A. El-Ganini, N. A. Saeed, and M. Eissa, 2013. Positive position feedback (PPF) controller for suppression on nonlinear system vibration. Nonlinear Dyn., 72, 517-537.
[7]	N. A. Saeed, W. A. El-Ganini, and M. Eissa, 2013. Nonlinear time delay saturation-based controller for suppression of nonlinear beam vibrations. App. Math. Model, 37, 8846–8864.
[8]	M. Eissa and Y. A. Amer, 2004. Vibration control of a cantilever beam subject to both external and parametric excitation. Appl. Math. Comput. 152, 611-619.
[9]	Y-Z. Zhao, and J. Xu, 2007. Effects of delayed feedback control on nonlinear vibration absorber system. J. Sound Vib., 308, 212-230.
[10]	U. H. Hegazy, 2009, Dynamics and control of a self-sustained electromechanical seismograph with time-varying stiffness. Mecanica, 44, 355-368
[11]	M. Yaman, 2009, Direct and parametric excitation of a nonlinear cantilever beam of varying orientation with time-delay feedback. J. Sound Vib., 324, 892-902.
[12]	M. Siewe Siewe and U. H. Hegazy, 2011, Homoclinic bifurcation and chaos control in MEMS resonators. 35, 5533-5552.
[13]	A. A. Nanha Djanan, B. R. Nana Nbendjo and P. Woafo, 2011, Control of vibration on a hinged-hinged beam under a non-ideal excitation using RLC circuit with variable capacitance. Nonlinear Dyn. 63(3), 447-489.
[14]	L-G. Wang, X. Zhang, D. Xu and W. Huang, 2012, Study of differential control method for solving chaotic solutions of nonlinear dynamic system. Nonlinear Dyn. 67(4), 2821-2833.
[15]	M. Moghaddas, E. Esmailzadeh, R. Sedaghati and P. Khosravi, 2012, Vibration control of Timoshenko beam traversed by moving vehicle using optimized tuned mass damper. J. Vib. Control. 18(6), 757-773.
[16]	I. Kucuk and I. sadek, 2013, Optimal time-delayed boundary control of beams using wavelets. J. Vib. Control. 19(14), 2083-2091.
[17]	K. A. Alhazza and M. A. Majeed, 2012, Free vibrations control of a cantilever beam using combined time delay feedback. J. Vib. Control. 18(5), 609-621.
[18]	Q. C. Nguyen and K-S. Hong, 2012, Simultaneous control of longitudinal and transverse vibrations of an axially moving string with velocity tracking. J. sound Vib. 331(13), 3006-3019.
[19]	C. Shin, C. Hong and W. B. Jeong, 2012, Active vibration control of bram structures using acceleration feedback control with piezoceramic actuators. J. sound Vib. 331(6), 1257-1269.
[20]	Z. N. Ahmadabadi and S. E. Khadem, 2012, Nonlinear vibration control of a cantilever beam by a nonlinear energy sink. Mech. Machine Theory. 50, 134-149.