Nonlinear Dynamic Analysis of a 1:2 Internally Resonant V-shaped Harvester

The objective of the manuscript is to explore the effects of geometry on the dynamics of an internally resonant vibrational energy harvester (VEH). Recently, the authors of this manuscript unveiled the existence of infinity(6N) solutions to design multi-members resonators which exhibit N commensurate frequencies equal to the number of members of the structure. The generalized topology of this family of resonators which exhibit 1:2 resonance resembles a V-shaped structure, i.e., a structure with two members adjoined at an angle phi, denoted as the folding angle. The classic 1:2 internally resonant L-shaped structure is a subset of solutions in this family. This work investigates the effect of the folding angle on the dynamic response of these oscillators. The nonlinear equations of motion are derived by means of Lagrange's equation, the beams are inextensible yielding second order nonlinearities. Approximate solutions of the model are obtained using the method of multiple scales. The effect of the folding angle on the nonlinear modal interaction in the power- frequency response curves is investigated.