Semi-analytical solution of random response for nonlinear vibration energy harvesters

Due to the prominent broadband performance of nonlinear vibration energy harvester, theoretical evaluations for the mean-square response to random excitations and the associated mean output power are of great interest. By employing the generalized harmonic transformation and equivalent nonlinearization technique, established here is a semi-analytical solution of random response for nonlinear vibration energy harvesters subjected to Gaussian white noise excitation. The semi-analytical solution for stationary probability density of the system response is obtained by two iterative processes. Numerical results for a Duffing-type harvester demonstrate rapid convergence of the iterative processes and high evaluation accuracy for the mean-square response and the mean output power. Furthermore, the influence of harvesting circuit on the mechanical subsystem can be converted to modified quasi-linear damping and stiffness with energy-dependent coefficients, which is different from the traditional viewpoint on the equivalence of constant-coefficient damping and provides more comprehensive explanation on the influence of harvesting circuit.