Pendulum energy converter excited by random loads

We present new solutions for the dynamics of a pendulum energy converter which is vertically excited at its suspension point. Thereby, we deal with a random excitation by a non-white Gaussian stochastic process. We formulate the pendulum energy converter as a weakly perturbed Hamiltonian system. The random process across the energy levels of the Hamiltonian system is then approximated by a Markov process, which is obtained by stochastic averaging. This procedure leads to analytical results for the energy of the pendulum motion, which are used for analyzing the required probability of reaching higher energy states of the pendulum energy converter in order to maximize the harvested energy.