Analytical study of anisimkin´s (quasilongitudinal) modes in piezoelectric plate

This paper presents a mathematical analysis of quasilongitudinal (QL) modes in piezoelectric quartz plate, which was found numerically and verified experimentally by Anisimkin in 2004. A new matrix formulation of analysis is used to compare pure elastic, piezoelectrically stiffened (with electrodes) and piezoelectrically unstiffened (without electrodes) cases. An approximate formulas to yield “allowed bands” for QL-modes is obtained. The formulas also covers newly found quasishear (QS) modes. Refined profiles of displacements through the plate thickness are presented to solve a mystery of little jumps in their profiles of longitudinal displacement.