Design optimization of damping material-inlaid plates for vibration control

Inlay structures composed of matrix and inlaid materials can be applied for vibration control in engineering structures, especially when the inlaid material has high damping property. In this work, we develop a shape optimization method of damping material-inlaid plates considering a frequency response problem in forced vibration. The squared displacement error norm of a designated evaluation point is used as the objective function and is minimized under an area constraint. In the shape optimization process, we carry out frequency response analysis to calculate shape gradient function, and then use the shape gradient functions in velocity analysis to update the shape or position of the inlaid material based on the H1 gradient method. This process is repeated for determining the optimal shape or position of the inlaid material. The optimal results of numerical examples showed that the developed design optimization method of inlay structures could significantly reduce the squared displacement error norm of an arbitrary designated evaluation point at an arbitrary specific frequency.