Isogeometric optimization of piezoelectric functionally graded material for energy harvester

Improving the energy harvesting efficiency of piezoelectric energy harvesters (PEHs) in the scientific domain is essential for the application of self-powered microelectromechanical devices. This paper proposes an isogeometric optimization method to optimize the material distribution of piezoelectric functionally graded material (PFGM) energy harvester. Firstly, we establish the isogeometric formulation of the PFGM energy harvester based on the plane strain hypothesis and Hamilton's principle. Meanwhile, the same non-uniform rational Bsplines basis functions are utilized to represent the distribution of the PFGM. Secondly, three optimization models with the specified eigenfrequency and maximum energy conversion efficiency as objective functions are established. Then we derive the analytical sensitivities by the adjoint method and use the method of moving asymptotes to update the design variables. Furthermore, several numerical examples are performed to study the convergence and accuracy of the numerical solutions and analyze the effects of the metallic volume ratio constraint and the initial design domain on the optimized material distribution. More importantly, the dynamic analysis is executed to further test the energy harvesting efficiency based on the optimized designs. The results show that the presented approach can not only realize the specified eigenfrequency but also effectively improve the energy harvesting efficiency.