Optimal design of material microstructure for maximizing damping dissipation velocity of piezoelectric composite beam

The topology optimization method of material microstructure of piezoelectric composite structures is proposed so as to improve the dynamic characteristics of the closed-loop system. The topology optimization model of material microstructure is built, where the design variable is constructed based on the SIMP interpolation scheme and the objective function is to maximize the damping dissipation velocity of the piezoelectric composite structure based on the independent modal control strategy, while the constraints are applied on the volume fractions of the phase materials. The sensitivity formulations of the damping dissipation velocity in modal space with respect to the design variables are derived. A bi-direction evolutionary structural optimization (BESO) method is developed to obtain a clear and optimal topology for material microstructure. The results of several numerical examples show that different initial designs of the base cell, different boundary conditions and the property of the disturbance have effect on the optimal solution. Also, the proposed method can effectively improve the active control performance and reduce structural weight.