Optimal design of cubic nonlinear energy harvester device for random vibrations

Linear energy harvesters have a narrow frequency bandwidth and hence operate efficiently only when the excitation frequency is very close to the fundamental frequency of the harvester. Consequently, small variations of the excitation frequency around the harvester's fundamental frequency drop the energy output making the harvesting process inefficient. To extend the harvester's bandwidth, some recent solutions call for using electromechanical devices with stiffness-type nonlinearities. This work deals with the optimisation of the performance of a single degree-of-freedom electromagnetic energy harvester whose mechanical behaviour has a Duffing-type nonlinearity, as for suspended masses, to reduce the size of energy harvesting devices without affecting their power output. The vibration input is assumed as a broadband Gaussian white noise base acceleration. It is analytically shown that the optimum load resistance of the device is different to that which is dictated by the principle of impedance matching.