Shear transverse acoustic wave

Slip is not always a purely dissipative process, and some energy can be stored at the solid-liquid interface. In the case that storage and dissipation at the interface are independent processes, a two-parameter slip model can be used. This can occur for a surface oscillating in the shear direction. Such a situation involves bulk-mode acoustic wave devices operating in liquid, which is where our interest in hydrodynamic couphng effects stems from. This type of sensor, an example of which is the transverse-shear mode acoustic wave device, the oft-quoted quartz crystal microbalance (QCM), measures changes in acoustic properties, such as resonant frequency and dissipation, in response to perturbations at the surface-liquid interface of the device. 

To model this, Duncan-Hewitt and Thompson [50] developed a four-layer model for a transverse-shear mode acoustic wave sensor with one face immersed in a liquid, comprised of a solid substrate (quartz/electrode) layer, an ordered surface-adjacent layer, a thin transition layer, and the bulk liquid layer. The ordered surface-adjacent layer was assumed to be more structured than the bulk, with a greater density and viscosity. For the transition layer, based on an expansion of the analysis of Tolstoi [3] and then Blake [12], the authors developed a model based on the nucleation of vacancies in the layer caused by shear stress in the liquid. The aim of this work was to explore the concept of graded surface and liquid properties, as well as their effect on observable boundary conditions. They calculated the hrst-order rate of deformation, as the product of the rate constant of densities and the concentration of vacancies in the liquid. 

J. S.Ellis and G. L. Hayward, Interfacial slip on a transverse-shear mode acoustic wave device,/ Appl Phys., 94, 7856-7867 [2003]. 

Figure 4. Theoretical trends for —(storage) and dissipation as the inner slip is varied between no slip (0) and strong slip (1) for a coated transverse shear acoustic wave device in water. The thickness of the film is 5 nm. The solid line displays the decrease in storage, and the dashed line shows the change in dissipation.

The propagation of linear acoustic waves in solids depends on two laws discovered by two of the most illustrious physicists of the seventeenth century, one from Cambridge and the other from Oxford. Consider a volume element of an isotropic solid subjected to shear, as shown in Fig. 6.1. If the displacement in the transverse direction is , and the component of shear stress in that direction is os, then Newton s second law may be written... 

Piezoelectric acoustic wave devices also respond to small changes in mass at surfaces immersed in (viscous) liquids [9]. The resonance frequency of AT-cut quartz resonators immersed in liquids depends on the liquid density and viscosity. The transverse shear wave which penetrates into the viscoelastic deposit and into the liquid is damped due to energy dissipation associated with the viscosity of the medium (film or liquid) at the acoustic frequencies. 

Figure 2.1 Pictorial representations of elastic waves in solids. Motions of groups of atoms ate depicted in these cross-sectional views of plane elastic waves propagating to the right. Vertical and horizontal displacements are exaggerated for clarity. Typical wave speeds, Vp, are shown below each sketch, (a) Bulk longitudinal (compressional) wave in unbounded solid, (b) Bulk transverse (shear) wave in unbounded solid, (c) Surface acoustic wave (SAW) in semi-infinite solid, where wave motion extends below the surface to a depth of about one wavelength, (d) Waves in thin solid plates.

Real ropes and strings have a measurable thickness and can also support torsion vibrations, due to the moment of inertia and the shear modulus of the string. Compression (longitudinal scalar) and shear (transverse vector) are the two fundamental forces and motions in ultrasonic and acoustic waves. 

Generally, the cut angle of quartz crystal determines the mode of induced mechanical vibration of resonator. Resonators based on the AT-cut quartz crystal with an angle of 35.25° to the optical z-axis would operate in a thickness shear mode (TSM) (Fig. 1.1) [4]. Clearly, the shear wave is a transverse wave, that is, it oscillates in the horizontal direction (jc-axis) but propagates in the vertical direction (y-axis). When acoustic waves propagate through a one-dimensional medium, the wave function (ij/) can be described by [11] ... 

Figure 2 Modes of acoustic propagation (A) longitudinal or compressional wave (B) transverse or shear wave (C) surface or Rayleigh wave and (D) plate or Lamb wave (symmetric mode).

---