Load Optimization of a Nonlinear Mono-Stable Duffing-Type Harvester Operating in a White Noise Environment

This paper investigates electric load optimization of nonlinear mono-stable Duffing energy harvesters subjected to white Gaussian excitations. Both symmetric and asymmetric nonlinear restoring forces are considered. Statistical linearization is utilized to obtain an approximate analytical expression for the optimal load as function of the other systems parameters. It is shown that the optimal load is dependent on the nonlinearity unless the ratio between the harvesting circuit time constant and the period of the mechanical oscillator is very large. Under optimal loading conditions, a harvester with a symmetric nonlinear restoring force can never produce more power than an equivalent linear harvester regardless of the magnitude or nature of the nonlinearity. On the other hand, asymmetries in the restoring force are shown to provide performance enhancement over an equivalent linear harvester.