Dynamics of a non-smooth type hybrid energy harvester with nonlinear magnetic coupling

In this paper, a system with energy harvester behavior is modeled by non-smooth coupled oscillators subjected to harmonic and random excitations. A modified harmonic balance method is proposed to study the dynamics of the oscillators under harmonic driving. Then, the probabilistic response of the system under bounded and colored noise excitations is tackled through the stochastic averaging method. We show that the proposed modified harmonic balance technique is very effective in parameters regime for which the system output waveform is nearly sinusoidal. In this parameters regime, the harvester performance is improved for optimum nonlinear magnetic coupling coefficients and for weak nonlinearities and damping in the harvester mechanical part. Under random excitations, we find in the weak parameters regime that, the probability density functions (PDFs) for the coupled oscillators amplitudes illustrate a single-peak mode and exhibit phenomenological transitions as the noisy excitations parameters vary. The mean output powers (MOPs) linearly increase with the colored noises intensities, and the piezoelectric MOP especially shows a resonance effect as the bounded noise level increases. Contrariwise, probed with Monte Carlo simulation, we find that the system exhibits the stochastic P-bifurcation for large parameters of coupling and nonlinearity; parameters’ regime for which the harvester under purely harmonic driving demonstrates low performance.