A velocity field level set method for topology optimization of piezoelectric layer on the plate with active vibration control

Vibration control has significant applications in many engineering areas to achieve designed vibration performances or suppress structural fatigue and failure. This paper presents a velocity field level set method for topology optimization of the piezoelectric layer on a plate with active vibration control. The material distribution of the piezoelectric layer and the topology optimization model for this problem is formulated in the level set framework, which can precisely track the layout (topology/shape) of piezoelectric layers with clear/smooth boundaries. Compared with the density-based method, the level set method can avoid the difficulties in the definition of material distributions and piezoelectric material properties for intermediate densities, which also leads to more accurate vibration control. We employ the constant gain velocity feedback as the vibration control algorithm. The dynamic compliance is set as the objective function and treated as the index representing the plate's vibration level. Using the velocity field level set method can map the original variational boundary shape optimization problem into the finite dimensional space and solve the optimization problem efficiently by general optimizers. We also show that the self-adjoint scheme can be used in the sensitivity analysis, which avoids solving additional adjoint problems. To verify the validity and efficiency of the proposed method, we give three numerical examples, in which the influence of the external frequency and the constant gain coefficient on optimization results are also discussed.