Exact dynamics of an angle-shaped resonator for energy scavenging applications

This manuscript details the derivation and solution of the equations of motion of angle-shaped resonators, composed of two prismatic members attached at various angles. The first part of the paper is devoted to the derivation of the analytical solution for the dynamic of a two member structure. The governing equation and the boundary conditions are derived by taking the variation of the Hamiltonian. The boundary value problem is then solved analytically giving rise to the characteristic equation of the system. In order to assess the validity of the analytical model presented, the analytical solution is compared against a semi-analytical model, finite element analysis and experiments. In the second part of the manuscript, we derive the electro-mechanical equation of motion of the angle-shaped resonator. The behavior of the harvester when subjected to single and multiple harmonic excitation is investigated along with the sensitivity onto the power harvested due to the folding angle.