A New Mass Sensor Based on Thickness-Twist Edge Modes in a Piezoelectric Plate

We propose a new mass sensor based on thickness-twist edge modes in a piezoelectric plate of 6mm crystals. By performing a theoretical analysis, a simple expression of sensitivity is obtained. The proposed sensor has an important advantage in the sense that it can be mounted away from the edge of the plate where the motion is insignificant and, thus, the operation of the device is unaffected. Copyright c © EPLA, 2007 Edge modes in plates and wedges are often used for resonators and acoustic wave sensors [1–5]. Compared to resonators based on bulk acoustic waves operating with infinite plate thickness-shear and thickness-stretch modes which have edge effects due to the finite sizes of real devices, edge modes are exact at the edge. An important advantage of edge modes is that away from the edge there is little motion, where mounting of the device can be achieved without affecting the device performance. The traditionally known edge modes are plate flexural [1,2] and thickness-stretch modes [3]. Recently edge thicknesstwist modes in a piezoelectric plate of 6mm crystals have been shown to exist [6]. The availability of these new edge modes suggests the possibility of producing new acoustic wave sensors with advantages. The objective of the present study is to show that new mass sensors can be made based on thickness-twist edge modes. In the study of acoustic wave mass sensors, researchers have been exploring various structures and modes to make different sensors. Some recent examples are the torsional and shear modes of shells [7,8]. Thickness-twist vibration modes of crystal plates are often used as the operating modes for resonators [9,10]. In addition to quartz plates which have been used for a long time, recently AlN and ZnO plates are of growing interest [11,12]. They are crystals of 6mm symmetry. Plates with normal and in-plane six-fold axes are both being developed. Polarized ceramics like PZT are transversely isotropic and the material matrices for their linear behavior have the same structures as those of 6mm crystals. Our analysis below is valid for both 6mm crystals and polarized ceramics. Consider the semi-infinite piezoelectric plate in fig. 1. The six-fold axis (or the poling direction of ceramics) is along x3. The two major surfaces at x2 =±h are tractionfree and are unelectroded. Thickness-twist motions of the plate are governed by u1 = u2 = 0, u3 = u(x1, x2, t), φ= φ(x1, x2, t), (1) where u is the displacement vector and φ is the electric potential. A function ψ can be introduced through [10,13]