analytical solution and optimization for energy harvesting from nonlinear vibration of magneto- electro- elastic plate

In the present paper, a mathematical model has been provided for a magneto-electroelastic plate to investigate its energy harvesting in nonlinear transverse vibration. the nonlinear equations of motion of a magneto-electro-elastic plate have been used based on the kirchhoff plate theory. these equations have been reduced to an ordinary deferential equations using airy stress function and galerkin method. the equivalent electrical circuit of the structure is developed. a closed form solution has been obtained for the output power of the harvester using the method of multiple scales. the obtained results are compared with those of finite element method and a good agreement observed between the results of displacement and voltage. by introducing an analytical relation for the power as cost function, the genetic algorithm method is applied to optimize the best parameters of the harvester which gives the maximum power. the effect of various parameters of the harvester, such as dimension and thickness, on the power is investigated and the results are discussed.