Parallel Finite Element Analysis Of Quartz Crystal Resonators With Considerations Of Complications

Quartz crystal resonators are essential components of electrical devices forfrequency control, whose frequency shift caused by many factors should be strictlylimited into a reasonable band for required performances in applications. This thesisstudied three major effects on vibrations of quartz crystal resonators, which includeenvironmental temperatures, piezoelectricity in the analysis of forced vibrations, andkinematic and material nonlinearities of quartz crystal plates. We introduced linearand nonlinear complications considered in the frame work of the Mindlin platetheory and their finite element formulation. Furthermore, some stable and reliablehigh performance computational parallel software packages are integrated to solvethe extremely large scale eigensystems and linear systems.We start by illustrating parallel finite element analysis and large scaleeigensystems and linear systems from finite element analysis of quartz crystalresonators. Solution algorithms and their corresponding solvers are chosenaccording to the needs of analyses of resonators. Then we demonstrate the Mindlinplate theory with thermal effect and its correction factors and displacementtruncation. After finite element formulation, quartz crystal resonators are analyzedby the coupled generalized eigensolver through their frequency spectra,frequency-temperature relations and the distribution of thickness-shear vibrations.Based on the piezoelectric Mindlin plate theory, we obtained its finite elementformulation with electrical variables included. Forced vibrations of quartz crystalresonators are investigated by a linear solver. Curves of capacitance ratios tofrequencies of currents are plotted. Finally, we formulated the nonlinear Mindlinplate theory into finite element analysis. Nonlinear high frequency vibrations ofquartz crystal plates are analyzed by a generalized nonlinear eigensolver. Weobtained frequency-amplitude relations and compared thickness-shear deformationswith different amplitudes. The MPI based parallel finite element software from this thesis work hassuccessfully completed lots of computations in LINUX clusters. Results from linearanalysis are almost the same as experimental data and commercial finite elementanalyses. Curves from nonlinear analysis are close to theoretical analysis. Thisefficient software with its accurate results will play an important role in the designof quartz crystal resonators.