Energy harvesting from a cantilever beam with a spring-loaded oscillating mass system and base excitation

The present study deals with the mathematical modeling of a nonlinear energy harvester (EH) to analyze it's frequency bandwidth for optimal use. The exhibited unique piezoelectric energy harvester (PEH) contains a cantilever beam as resonator with a moving mass. To fulfill the mechanism, the mass needs to be connected to the fixed end of the beam with a spring that acts as a mechanical amplifier. A novel analytical approach with 1:2 internal resonance (IR) including kinematic nonlinearity is addressed for energy harvesting. The occurrence of strong nonlinear coupling is the result of constant interconnection between the beam and moving mass. A discrete electro-mechanical coupled equation is derived using Galerkin's method followed by Hamilton's energy method. To analyze the effect of input parameters on the frequency bandwidth, MATLAB code is improved by implementing the “Method of multiple scales” (MMS) for furthering the energy output of the system. Due to IR, the solution tilted to two branches in the designed EH, witnessing broader frequency bandwidth. The influence of different system parameters such as spring stiffness, mass, and velocity of moving mass changed the position of central frequency resulting in the change in symmetry of frequency response.