TY - JOUR

T1 - ON THE USE OF 1-D FINITE ELEMENTS FOR THE TEMPERATURE BEHAVIOR OF A CONTOURED AND PARTIALLY PLATED SC-CUT RESONATOR.

AU - Yong, Y. K.

PY - 1987

Y1 - 1987

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0023534399&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023534399&partnerID=8YFLogxK

U2 - 10.1109/ultsym.1987.198982

DO - 10.1109/ultsym.1987.198982

M3 - Conference article

AN - SCOPUS:0023534399

SP - 353

EP - 358

JO - Ultrasonics Symposium Proceedings

JF - Ultrasonics Symposium Proceedings

SN - 0090-5607

ER -