Analytical Approximations To Resonance Response Of Strongly Forced Nonlinear Oscillators And Its Application

At present,many wireless devices work uninterrupted,however ordinary batteries cannot provide continuous power supply.Researchers have investigated many alternative types of power supplies to replace traditional batteries.Scavenging vibrational energy from the environment has attract many investigations.Here we select electromagnetic and piezoelectric energy harvester models for research.In order to analyze coupled electromechanical vibration system,the basic work is to solve the resonance response of a single-degree-of freedom nonlinear oscillator subjected to harmonic excitation.Methods for solving analytical approximate solutions of nonlinear vibration equations have limitations.The classical perturbation methods,such as the Lindstedt-Poincaré(LP)method,the averaging method,and the method of multiple scales(MS),require the presence of a small physical parameter in the governing equation.the analyses have been significantly retarded for strong nonlinear dynamical systems when nonlinearity becomes large.Oscillation system with non-odd nonlinearity can be more complicated.The perturbation method and the harmonic balance method can only provide good results under the assumption of weak nonlinearity.In this paper,Newton-HB method is proposed for constructing the approximate solution of the main resonance response of a strongly nonlinear vibration system under harmonic excitation.In the study of harmonically forced odd or non-odd nonlinear oscillation with single degree of freedom,the first approximation is presented based on single-term or two term HB method,then Newton method and HB method is cooperated to obtain a set linear algebraic equations,so that the complicated nonlinear algebraic equations given by high order HB method is avoided.The second approximation is obtained when the linear algebraic equations are solved,the stability analysis is given according to Floquet theory.The approximations obtained by Newton-HB method are compared with numerical simulation results and show good precision.The oscillators with odd and non-odd nonlinearities are discussed in practical examples.For No matter for vibration system with odd nonlinearity or non-odd nonlinearity,frequency responses of each harmonic terms can be established with good accuracy.Based on the analytical approximation method of forced vibration of single-degree-of-freedom nonlinear oscillator,Newton-HB method can be extended to the study of electromechanical coupled vibration of energy harvesting systems.With several examples,it can be concluded that the analytical solution obtained by Newton-HB method is of high accuracy for electromechanical coupled vibration systems with both odd and non-odd nonlinearities.