Sustained resonance in a linear oscillator is achievable with a drive whose constant frequency matches the resonant frequency of the oscillator. But in oscillators with nonlinear restoring forces such as the pendulum, Duffing and Duffing-Van der Pol oscillator, the resonant frequency changes as the amplitude changes, so a constant frequency drive results in a beat oscillation instead of sustain...

In this work, we present a method of generating class nonlinear ordinary differential equations (ODEs), representing the dynamics appropriate oscillators, that have characteristics either amplitude independent frequency oscillations or amplitude-dependent from integrals simple harmonic oscillator equation. To achieve this, consider case where are in same form both for linear and oscillators cas...

In this thesis, the performance criteria for the objective comparison of different classes of single-degree-of-freedom oscillators under stochastic excitation are developed. For each family of oscillators, these objective criteria take into account the maximum possible energy harvested for a given response level, which is a quantity that is directly connected to the size of the harvesting confi...