Two-dimensional analysis using 1D-FEM for straight-crested waves in arbitrary anisotropic crystal plates and axisymmetric piezoelectric vibrations in ceramic disks

We have developed a two-dimensional analysis using the one-dimensional finite element method (1D-FEM) for straight-crested waves in arbitrary anisotropic crystal plates and axisymmetric piezoelectric vibrations in ceramic disks. The solution of the two-dimensional equations of motion is described with a linear combination of eigenmodes guided by a pair of parallel edges. 1D-FEM is effectively used to determine the guided eigenmodes and the their amplitudes. The method attains a high degree of accuracy in spite of a small matrix size as compared with two-dimensional (2D) FEM. As examples of the method, the frequency spectra of straight-crested waves in SC-cut quartz crystal plates and axisymmetric piezoelectric vibrations in barium titanate (Ba-TiO₃) disks are represented. A convergence study is presented for BaTiO₃ disks. The frequency spectra of straight-crested waves in AT-cut quartz plates are also calculated with the aim of examining the accuracy of Mindlin´s plate equations for those waves