Harvesting energy from shock environments via functionally graded magneto-electro-elastic materials

Given the fact that the environmental kinetic energy may appear in the form of shock pulse excitation, this paper aims to investigate the response of a shock excited cantilever beam equipped with two symmetric functionally graded magneto-electro-elastic layers. To this end, employing a hybrid procedure including the Ritz method together with the geometric nonlinear Euler-Bernoulli beam theory, the coupled magneto-electro-mechanical reduced equations of motion are obtained. The model predictions are compared and successfully validated by those available in the literature. Having the vibration frequency of the system, which is obtained by the method of multiple time scales, the optimal duration maximizing the influence of shock pulse acceleration is predicted using the power shock spectrum introduced in this study for the first time. The results reveal that the harvested power maximizes when the system fundamental frequency becomes 1.36 times the equivalent shock frequency.