Thickness-shear vibration analysis of rectangular quartz plates by a numerical extended Kantorovich method

Thickness-shear vibration analysis of rectangular quartz plates was carried out by a numerical extended Kantorovich method (NEKM) proposed in this paper. Thickness-shear vibration is characterized by high frequency vibration that needs huge computational cost. The NEKM reduced the two-dimensional elasticity problem into two one-dimensional ones and then solved them iteratively as the Kantorovich method. But all the processes of reduction and solvation in NEKM were carried out by using a differential quadrature finite element method (DQFEM). Therefore, the NEKM is much simpler than the Kantorovich method that does all the processes analytically with great complexity. Because the two-dimensional problem was reduced to one-dimensional ones and the DQFEM was very accurate, the NEKM was very efficient and accurate. The correctness and high accuracy of the NEKM were validated through numerical comparison with the results of the Kantorovich method in literature.