Vibrations of Longitudinally Polarized Ferroelectric Cylindrical Tubes

Abstract

The theory of vibrations of longitudinally polarized, thin-wall ferroelectric ceramic tubes is derived including the lateral influence on the longitudinal vibrations. Tenors are utilized throughout the derivation, but a summary of the results is presented in the commonly used matrix forms. The equations of motion and the equations of state for materials possessing transverse isotropy are transformed to cylindrical coordinates. A new electromechanical equivalent circuit is obtained which is similar to that of Mason, except that the latter ignores lateral effects. The new theory explains experimental results which would be considered anomolous in the older one-dimensional theory.