Metamaterial based piezoelectric acoustic energy harvesting: Electromechanical coupled modeling and experimental validation

Piezoelectric energy harvesting technology utilizing acoustic metamaterials investigated by experiment and simulation improves the sound energy density and conversion efficiency. A fully coupled electromechanical model in both the mechanical and electric domains is crucial for accurate prediction and optimization of acoustic metamaterial based on sound energy harvesting. Based on the Kirchhoff thin plate theory, constitutive laws of isotropic aluminum substrate and transversely isotropic piezoelectric bimorph, the electromechanical coupled governing equation in the mechanical domain is deduced for a two-dimensional acoustic metamaterial based piezoelectric energy harvester. Each piezoelectric layer is represented as a current source in series with its internal capacitance for derivation of the electromechanical coupled governing equation in the electrical domain via Gauss’s law and Kirchhoff’s laws. With generalized boundary conditions, modal analysis is performed using the Galerkin method and Kelvin-Kirchhoff condition. The general transient response and frequency response functions are obtained under the excitation of sound waves and the reaction forces of the silicone rubbers. The time-history, power spectrum and phase portrait of the measured harvested voltage at 90 fixed frequencies agree well with the model predictions. The theoretical maximal harvested power is 3.09 mW, with the optimal resistance of 28180 Ω and inductance of 0.28H connected in parallel. Near the resonant frequency, the utilization rate of converting sound energy into electrical power is maximized. The proposed electromechanical coupled model can be used as a basis for further topology design and optimization and underlying physics for experimental study.