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This paper presented adifferential quadrature hierarchical finite element method (DQHFEM) and appliedit to thickness-shear vibration analysis of rectangular quartz plates. TheDQHFEM introduced the key ideas and skills of the differential quadraturefinite element method (DQFEM) into the hierarchical finite element method(HFEM) to overcome the numerical stability problems and the difficulty incomputing high-order hierarchical elements in the HFEM. The incorporation ofthe DQFEM into the HFEM also improved its computational accuracy and efficiencydue to the simplicity and high accuracy of the DQFEM. The high frequencythickness-shear vibration of a rectangular quartz plate was modeled by usingseveral DQHFEM elements. The degrees of freedom of the DQHFEM elements were adjustedaccording to a balance between accuracy and computational cost. The DQHFEM, asan improved version of the HFEM, was shown to have the potential of becomingthe mainstream in developing finite element software in future.

Thickness-shear vibration, Quartz plate, Frequency, Differential quadrature method, Hierarchical finite element method