TOPOLOGY OPTIMIZATION OF PIEZOELECTRIC ACTUATOR CONSIDERING CONTROLLABILITY

Piezoelectric actuators can convert electrical energy into mechanical energy, and has application potential in active vibration control of structures. Since the layout of the piezoelectric actuators has a great influence on the vibration control effect, the optimization of the actuators has always been one of the key factors to structural control. In order to improve the efficiency of control energy in the piezoelectric structure, this paper proposes a topology optimization method for the layout design of piezoelectric actuators with the goal of improving structural controllability. The finite element modeling of the piezoelectric structure is carried out based on the classical laminate theory. The modal superposition method is used to map the dynamic governing equation to the modal space. The controllability index based on the singular value of the control matrix is derived. In the optimization model, the exponential form of the controllability index is chosen as the objective function, and the design variables are the relative densities of the actuator elements. Based on the Solid Isotropic Material Penalization method, an artificial piezoelectric coefficient penalty model is constructed. Sensitivity analysis for the controllability index is proposed based on the singular value of the control matrix. The optimization problem is solved by a gradient-based mathematical programming method. Numerical examples verify the effectiveness of the sensitivity analysis method and the optimization model and show the significance of the layout design of piezoelectric actuators. The influence of some key factors on the optimization results are discussed. It shows that the more piezoelectric materials, the better the controllability; the modes of interest in the objective function has a great influence on the layout of the piezoelectric actuators.