A nonlinear finite element analysis of high frequency vibrations of quartz crystal plates

We formulate the first-order nonlinear Mindlin plate equations in the finite element method to study the high frequency thickness-shear vibrations of quartz crystal plates. Iterative algorithms are utilized to solve the resulted nonlinear eigensystems. High performance computational software packages are integrated into our nonlinear finite element program to speed up the extremely large scale computations. We considered both kinematic and material nonlinearities in vibrations analyses, and obtained the frequency-amplitude relations. We also compared distributions of the thickness-shear deformation at different amplitudes. This nonlinear finite element software can be further improved to study nonlinear phenomena arising from miniaturized quartz crystal resonators.