Axisymmetric vibration of infinite piezoelectric cylinders using one-dimensional finite elements

A general finite-element analysis for infinite piezoelectric cylinders has been formulated. The classical three-dimensional elasticity equations of motion are used. The dependence on theta , z, and time are included by assuming appropriate trigonometric functions, and the three-dimensional problem is reduced to a one-dimensional finite element with four degrees of freedom per node. The tabulated results are limited to cylinders with stress-free, shorted electrode ( phi =0) boundary conditions at the outside surface of the cylinder. However, solutions for a variety of boundary conditions are possible. Solutions for the piezoelectric cylinder compare favorably with the existing literature. The motion of piezoelectric cylinders with thin coatings is analyzed by modeling the cylinder and thin coating as a layered cylinder.<>