Design Sensitivity Analysis and Topology Optimization of Piezoelectric Crystal Resonators

압전 수정진동자의 설계민감도 해석과 위상 최적설계

  • 하윤도 (서울대학교 조선해양공학과) ;
  • 조선호 (서울대학교 조선해양공학과) ;
  • 정상섭 ((주)빛샘정보통신)
  • Published : 2005.04.01


Using higher order Mindlin plates and piezoelectric materials, eigenvalue problems are considered. Since piezoelectric crystal resonators produce a proper amount of electric signal for a thickness-shear frequency, the objective is to decouple the thickness-shear mode from the others. Design variables are the bulk material densities corresponding to the mass of masking plates for electrodes. The design sensitivity expressions for the thickness-shear frequency and mode shape vector are derived using direct differentiation method(DDM). Using the developed design sensitivity analysis (DSA) method, we formulate a topology optimization problem whose objective function is to maximize the thickness-shear component of strain energy density at the thickness-shear mode. Constraints are the allowable volume and area of masking plate. Numerical examples show that the optimal design yields an improved mode shape and thickness-shear energy.