Optimal load resistance of a randomly excited nonlinear electromagnetic energy harvester with Coulomb friction

A nonlinear electromagnetic energy harvester directly powering a load resistance is considered in this manuscript. The nonlinearity includes the cubic stiffness and the unavoidable Coulomb friction, and the base excitation is confined to Gaussian white noise. Directly starting from the coupled equations, a novel procedure to evaluate the random responses and the mean output power is developed through the generalized harmonic transformation and the equivalent non-linearization technique. The dependence of the optimal ratio of the load resistance to the internal resistance and the associated optimal mean output power on the internal resistance of the coil is established. The principle of impedance matching is correct only when the internal resistance is infinity, and the optimal mean output power approaches an upper limit as the internal resistance is close to zero. The influence of the Coulomb friction on the optimal resistance ratio and the optimal mean output power is also investigated. It is proved that the Coulomb friction almost does not change the optimal resistance ratio although it prominently reduces the optimal mean output power.