A two-dimensional, Lagrangean variational equation of motion for the incremental displacements superposed on homogeneous thermal strains in an electrode plated crystal resonator was derived. A one-dimensional form of the equation was considered and solved using 1-D, cubic finite elements. The program was applied to the study of the f-T behavior of a contoured and partially plated SC-cut quartz strip. The variable thickness in a contoured strip was interpolated using the same cubic finite-element shape functions. Numerical convergence of the fundamental thickness shear frequency and its f-T curve was examined in meshes of increasing fineness. A preliminary study was performed of the thickness shear mode and its f-T curve with respect to the electrode thickness and contour, including both the plano-convex and plano-Gaussian contoured surfaces. The plano-Gaussian strip has more parameters than the plano-convex strip that can be used to control f-T behavior and energy trapping.
All Science Journal Classification (ASJC) codes