Random response of a two-degree-of-freedom rotational vibration energy harvester

The rotational vibration energy harvester is designed to convert the mechanical energy in the environment to useful electric energy. The vibration source in the nature is always broadband and implied randomness. To exploit the random dynamical characteristic of the rotational energy harvester, the steady-state response of a two-degree-of-freedom system under random excitation is investigated. The rotational component seems as an inerter, which induces an additional degree-of-freedom. Firstly, the linear system is analyzed, and the influence of the system parameters on the stationary mean-square response is discussed. The lower natural frequency of the primary system and higher natural frequency of the generator are good for improving the harvester’s performance. Then, the nonlinear stiffness is considered to show the nonlinear behavior of the energy harvester under random excitation. The stochastic averaging of quasi-non-integrable Hamilton system is applied to solve the steady-state probabilistic density function. The results show that the nonlinear stiffness plays a negligible role to the harvester. The comparison between the analytical and Monte-Carlo simulation results validates the accuracy of the proposed technique within a certain parameter range. When the parameters tend to a small value (i.e., ω2→1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega }_{2}\to 1$$\end{document}), the analytical results will deviate those from Monte-Carlo simulation, which is mainly due to the degeneration of the non-integrability of Hamilton system. Finally, in order to analyzing the situation of ω2→1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega }_{2}\to 1$$\end{document}, the equivalent linearization technique is adopted to evaluate the mean-square response and the output power. The accuracy of the results is good. For small frequency ω2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega }_{2}$$\end{document}, the output power is small.