On the optimization of the effective electromechanical coupling coefficients of a piezoelectric body

Effective electromechanical coupling coefficients are defined based on the expression for the internal energy of a piezoelectric body [B. S. Aronov, "Energy analysis of a piezoelectric body under nonuniform deformation," J. Acoust. Soc. Am. 113, 2638-2646 (2003)]. The condition is considered under which the effective coupling coefficient can be maximized up to the value of the material coupling coefficient for any given distribution of deformation. A simple practical way to optimize the effective coupling coefficient of a transducer by changing its electrode shape is illustrated with examples of transducers vibrating in longitudinal and flexural modes.