Two-dimensional analysis using one-dimensional FEM for straight-crested waves in arbitrary anisotropic crystal plates and axisymmetric piezoelectric vibrations in ceramic disks

We have developed a hybrid method applicable to straight-crested waves in arbitrary anisotropic crystal plates and to axisymmetric piezoelectric vibrations in ceramic disks. The solutions to two-dimensional (2-D) equations of motion are described with a linear combination of eigenmodes guided by a pair of parallel edges. The guided eigenmodes and their amplitudes are determined by using one-dimensional (1-D) finite element method (FEM). The method developed here provides rapid convergence with small matrix size compared with 2-D FEM. Computer programs have been developed for three examples, SC- and AT-cut quartz plates and barium titanate (BaTiO/sub 3/) disks, for which the frequency spectra and the corresponding mode shapes were calculated. The frequency spectra of AT-cut quartz plates are compared with those obtained from Mindlin's plate equations, with the aim of examining the accuracy of the straight-crested wave solutions for Mindlin's plate equations. A convergence study is also presented for BaTiO/sub 3/ disks.