Numerical Computations of Radial Vibrations of Axially Polarized Piezoelectric Circular Cylinder

Abstract

Influence of the initial stresses on the frequency equation and the natural frequencies for radial vibrations of axially polarized piezoelectric circular cylinder have been taken into account.

The mechanical boundary conditions correspond to those of stress free lateral surfaces while the electrical boundary conditions correspond to those of open and short circuit are considered. The satisfaction of the boundary conditions lead to the frequency equation, in the form of determinant involving Bessel functions, have been taken into consideration. The roots of the frequency equations give the values of the characteristic circular frequency parameters of the first three modes for various geometries. These roots are numerically computed and programmed for numerical evaluation by ''Bisection Method Iterations Technique (BMIT)'' and presented graphically for various thickness of the circular cylinder and for different values of the initial stress. The effect of the initial stress on the natural frequencies are illustrated graphically for a transversely isotropic piezoelectric martial PZT?4 circular cylinder.

It is found that both the thickness of the circular cylinder and the initial stress have a substantial effect on the dispersion behavior.

The results obtained in this paper may be applied to the vibrations of annular accelerometers operating in the radial shear mode. Also, they have theoretical basis application and have meaningful design for piezoelectric probes and electro-acoustic devices in the nondestructive evaluation.

Keywords: Piezoelectricity, frequency equation, Transverse surface waves, Initial stress, Hexagonal crystals.