Exact series model of axially polarized hollow piezoelectric ceramic cylinders of finite length.

An analytical model is presented of axisymmetric circular hollow piezoelectric ceramic cylinders with arbitrary dimensions and boundary conditions. Forced vibrations of the cylinders with specified potentials on the electroded surfaces and displacement or stress on the boundaries are considered. The exact, linearized, axisymmetric governing equations are used in the analysis. Three series solutions are used, and each term in each series is an exact solution to the exact governing equations of motion. The terms in the series expressions for components of displacement, stress, electric potential, and electrical displacement are products of Bessel and sinusoidal functions and are orthogonal to other terms. Complete sets of functions in the radial and axial directions are formed by terms in the first series and the other two, respectively. It is, therefore, possible to satisfy arbitrary boundary conditions on all surfaces of the hollow piezoelectric cylinder. Numerical results are presented for hollow piezoelectric cylinders of various dimensions. Input electrical admittance and displacements are computed for three special cases in bands that include several resonance frequencies, and they are in excellent agreement with those computed using atila-a finite element package.