Plate equations for piezoelectrically actuated flexural mode ultrasound transducers

This paper considers variational methods to derive two-dimensional plate equations for piezoelectrically actuated flexural mode ultrasound transducers. In the absence of analytical expressions for the equivalent circuit parameters of a flexural mode transducer, it is difficult to calculate its optimal parameters and dimensions, and to choose suitable materials. The influence of coupling between flexural and extensional deformation, and coupling between the structure and the acoustic volume on the dynamic response of piezoelectrically actuated flexural mode transducer is analyzed using variational methods. Variational methods are applied to derive two-dimensional plate equations for the transducer, and to calculate the coupled electromechanical field variables. In these methods, the variations across the thickness direction vanish by using the stress resultants. Thus, two-dimensional plate equations for a stepwise laminated circular plate are obtained.