Propagation of Thickness-Twist Waves in an Infinite Piezoelectric Plate

Thickness-twist waves in piezoelectric plates are widely used as the operating modes for acoustic wave resonators, filters, sensors, and other devices (Mindlin, 1965; Mindlin, 1967; Pearman, 1968; Bleustein, 1966; Bleustein, 1969; Yang et al., 2008a; Yang & Guo, 2006). Acoustic waves in these devices are driven by an alternating voltage applied to the electrodes deposited on the plates. Therefore there has been continuing research effort on the effect of electrodes (Ballato & Lukaszek, 1974; Kosinski, 2003; Wang & Shen, 2005; Yang et al., 2005). Recently, due to the need of device miniaturization, there has been growing research interest on electrode configurations. Electrodes of varying thickness have been used to adjust the vibration distribution in plates (Pao et al., 2007; Yang et al., 2007a; Wang et al., 2008). Electrode shape has also been analyzed for design optimization. In Yang et al. (2007b) it was shown that electrodes with corners cause field concentration and should be avoided in general. Optimal electrode size and shape were determined in Mindlin (1968) and Yang et al. (2008b). On the other hand, a vibrating elastic (or piezoelectric) body when put in contact with a viscous fluid changes its resonant frequencies due to the inertia and viscosity of the fluid. Equivalently, the speed of a propagating wave in a body in contact with a fluid is also affected by the fluid. This effect has been used to make various fluid sensors for measuring fluid viscosity or density (Kanazawa & Gordon, 1985; Josse et al., 1990; Reed et al., 2001; Kim et al., 1991; Vogt et al., 2004; Guo & Sun, 2008; Peng et al., 2006). More references can be found in a review article (Benes et al., 1995). For fluid sensor applications, vibration modes of a body without a normal displacement at its surface are of general interest. Thickness-shear and thickness-twist modes in a plate (Kanazawa & Gordon, 1985; Josse et al., 1990; Reed et al., 2001), torsional modes of a circular shaft (Kim et al., 1991; Vogt et al., 2004), and anti-plane surface waves (Guo & Sun, 2008; Peng et al., 2006) are modes with tangential surface displacements only and have been used for fluid sensor applications. To establish the relation between wave frequency and fluid density or viscosity, a coupled problem of fluid-structure interaction needs to be solved. This usually