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-Electro-Elastic (MEE) plate to investigate its energy harvesting in nonlinear transverse vibration. The nonlinear equations of motion of an MEE plate have been used based on the Kirchhoff plate theory. These equations have been reduced to an ordinary differential equation using the Airy stress function and Galerkin Method. Also, two other equations have been made using electrical and magnetic aspects of the structure. Then, the equivalent electrical and magnetic circuit of the structure is developed. There are three ordinary differential equations that need to be solved together. 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 FEM and a good agreement observed between the results of isplacement and voltage. By introducing an analytical relation for the power as a 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.