3D analysis of thickness vibrations in doubly rotated contoured quartz plates

Quasi-thickness modes occurring in contoured piezoelectric plates of any orientation may be predicted by various kinds of analysis. Among them are the fully analytic method proposed by D.S. Stevens and H.F. Tierston (1986), the finite elements (FE) method (fully numeric), as proposed by various commercial programs, and the modal decomposition method (mixed method, analytic and numeric) developed by B. Dulmet (1991). Although they are not negligible, the computational requirements of the latter method are found to be considerably lower than those involved by FE method to get similar results. Some X-ray topographs performed on a SC-cut sample are presented to rate the respective accuracy of the three models to predict the orientation of anharmonic modes patterns around the plate normal