Resonance and vibration control of two-degree-of-freedom nonlinear electromechanical system with harmonic excitation

The dynamics and chaos control of the two-degree-of-freedom nonlinear electromechanical system, in which the magnetic field is modeled as being time-varying (periodic in fact), will be investigated. The system is modeled by a coupled second-order nonlinear ordinary differential equations. Their approximate solutions are sought applying the method of multiple scales. A reduced system of four first-order 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 steady-state response and stability of the solutions for various parameters are studied numerically, using the frequency response function and the time-series solution. Effects of system parameters including external forces and time-varying magnetic field on the solutions of nonlinear equations are investigated numerically. The amplitudes have maximum peaks at the simultaneous primary resonance case \(({\varOmega } = \omega _{1}=\omega _{2}=\omega =1.0)\) 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.