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Title of Journal: Nonlinear Dyn

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Abbravation: Nonlinear Dynamics

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Springer Netherlands

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1573-269X

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Resonance and vibration control of twodegreeoff

Authors: Y A Amer
Publish Date: 2015/05/08
Volume: 81, Issue: 4, Pages: 2003-2019
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Abstract

The dynamics and chaos control of the twodegreeoffreedom nonlinear electromechanical system in which the magnetic field is modeled as being timevarying periodic in fact will be investigated The system is modeled by a coupled secondorder nonlinear ordinary differential equations Their approximate solutions are sought applying the method of multiple scales A reduced system of four firstorder ordinary differential equations is determined to describe the time variation of the amplitudes and phases of the vibration in the mechanical and electrical components of the considered model The steadystate response and stability of the solutions for various parameters are studied numerically using the frequency response function and the timeseries solution Effects of system parameters including external forces and timevarying magnetic field on the solutions of nonlinear equations are investigated numerically The amplitudes have maximum peaks at the simultaneous primary resonance case varOmega = omega 1=omega 2=omega =10 and hence is considered as the worst resonance case of the system behavior It can be seen that the best control law is the negative linear velocity feedback Comparison between numerical solution and perturbation solution is obtained

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