We consider a vibrating system with piezoelectric patches whose minimum vibration frequency is to be minimized subject to some constraint on the patch geometry. A numerical scheme is constructed using the level set method devised in  and the projected gradient method devised in  to optimize the patch geometry. An integral equation approach introduced in [4, 17, 20, 21] is also presented for the computation of the corresponding eigenvalue problem.
"Level Set Method for Shape Optimization of Plate Piezoelectric Patches." Methods Appl. Anal. 10 (2) 329 - 346, June 2003.