Eigenfrequencies of a 3D piezoelectric cylinder

摘要

free vibrations of a solid 3D piezoelectric cylinder of class 6mm are investigated. First the equations of motion are reformulated with the help of three scalar potentials. This decouples the SH waves and is done in a way which is coordinate-free in the transverse coordinates. Next the modes in an infinite plate are derived in crylindrical coordinates, and this involves Bassel functions in the radial direction. A superposition of these modes is then used to form the eighenmodes of the cylinder with a finite radius. The remaining lateral boundary conditions give a determinantal condition for the eigenfrequencies. Numerical results are given and are compared with previous published results.