Computing Vibration Eigenmodes in Piezoelectric Ceramic Resonators Discretized by the Energy-Orthogonal Fifteen-Nodes Pentahedral Finite Element

This contribution studies the propagation of bulk acoustic waves in piezoelectric ceramics discretized by the finite element method. Specifically, the fifteen-nodes pentahedral finite element is selected. The element elastic and dielectric stiffness matrices are split into basic and higher order components which are related to the mean and deviatoric components of the element strain and electric fields, respectively. This decomposition is applied to the total energy of the finite element assemblage. By a dispersion analysis the higher order total energy is related to the total energy error and the number of elements per wavelength. As application to piezoelectric ceramic resonators, by the higher order total energy, vibration eigenmodes accurately captured by a finite element model will be identified. Then, by energy arguments, those eigenmodes will be physically characterized.