Transverse shear mode

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. 

More recently methods have also been developed to measure the adsorbed amount on single surfaces and not onto powders. Adsorption to isolated surfaces can, for instance, be measured with a quartz crystal microbalance (QCM) [383]. The quartz crystal microbalance consists of a thin quartz crystal that is plated with electrodes on the top and bottom (Fig. 9.11). Since quartz is a piezoelectric material, the crystal can be deformed by an external voltage. By applying an AC voltage across the electrodes, the crystal can be excited to oscillate in a transverse shear mode at its resonance frequency. This resonance frequency is highly sensitive to the total oscillating mass. For an adsorption measurement, the surface is mounted on such a quartz crystal microbalance. Upon adsorption, the mass increases, which lowers the resonance frequency. This reduction of the resonance frequency is measured and the mass increase is calculated [384-387],... 

DETECTION OF PROTEIN-APTAMER INTERACTIONS BY MEANS OF ELECTROCHEMICAL INDICATORS AND TRANSVERSE SHEAR MODE METHOD... 

More complete theories of the operation of transverse shear mode resonators have been given by Kanazawa [11,12], Martin et al, [13,14], Lucklum and Hauptmann [15-17], Voinova, Jonson andKasemo [18], Johannsmann [19,20], Tsionsky [21] and Amau [22], In these theories, the electrical impedance of the QCM, Z, is complex. The impedance of a TSM resonator damped by a finite viscoelastic film can be described as the sum of two complex impedances ... 

IS THE TRANSVERSE SHEAR MODE RESONATOR A TRUE MICROBALANCE ... 

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

A sdiematic of our experimental setup is shown in Fig. 1. Isotherms are recorded by monitoring adsorption onto metal electrodes which we have evaporated onto the major surfaces of a quartz crystal oscillator which vibrates in a transverse-shear mode. The crystal is driven at its resonant frequency by means of a Pierce oscillator circuit (ref. 13). Changes in frequency are proportional to the quantity of gas adsorbed (ref. 14), so an isotherm is a plot of frequency shift versus pressure at fixed temperature. The microbalance crystals for these studies were polished single crystals of quartz which had quality factors near 10 (ref. 15). We produced the electrodes by evaporation of 99.999% pure Ag or Au at 5 X 10 torr onto the faces of the quartz blanks. The temperature of the substrate was variable between 80 and 500 K. The deposition rate was variable between. 5 and 76 A/s. 

Other researchers have substantially advanced the state of the art of fracture mechanics applied to composite materials. Tetelman [6-15] and Corten [6-16] discuss fracture mechanics from the point of view of micromechanics. Sih and Chen [6-17] treat the mixed-mode fracture problem for noncollinear crack propagation. Waddoups, Eisenmann, and Kaminski [6-18] and Konish, Swedlow, and Cruse [6-19] extend the concepts of fracture mechanics to laminates. Impact resistance of unidirectional composites is discussed by Chamis, Hanson, and Serafini [6-20]. They use strain energy and fracture strength concepts along with micromechanics to assess impact resistance in longitudinal, transverse, and shear modes. 

The shear mode involves the application of a load to a material specimen in such a way that cubic volume elements of the material comprising the specimen become distorted, their volume remaining constant, but with opposite faces sliding sideways with respect to each other. Shear deformation occurs in structural elements subjected to torsional loads and in short beams subjected to transverse loads. 

The failure mechanisms of interest in reinforced masonry wall elements include flexural, transverse shear, in-plane shear and in some cases, combined axial compression and flexure. Buckling failure modes of compression elements and connection failures are to be avoided. 

One of the most important properties which control the damage tolerance under impact loading and the CAI is the failure strain of the matrix resin (see Fig. 8.8). The matrix failure strain influences the critical transverse strain level at which transverse cracks initiate in shear mode under impact loading, and the resistance to further delamination in predominantly opening mode under subsequent compressive loading (Hirschbuehler, 1987 Evans and Masters, 1987 Masters, 1987a, b Recker et al., 1990). The CAI of near quasi-isotropic composite laminates which are reinforced with AS-4 carbon fibers of volume fractions in the range of 65-69% has... 

In some gels, the frequency-dependence of the shear modulus is appreciable even at low frequencies as will be discussed in the next section. Then, the transverse sound mode becomes strongly damped. 

The quartz crystal micro-balance (QCM), the most extensively studied shear mode AT-cut quartz resonator, is comprised of a thin slice of quartz single crystal with two metal electrodes deposited on both faces of the crystal. These excitation electrodes generate a transverse shear wave across the thickness of the crystal that propagates into the film immobilized onto the crystal surface. When the over-layer is non-rigidly coupled to the... 

Figure 3.39 (page 114) shows the phase velocities of the waves as a function of the product k4, where k, = 27t/A, A, is the wavelength of the bulk transverse (shear) wave in the medium of which the plate is made, and d is the plate thickness. The waves divide naturally into two sets symmetric waves (denoted by So, S],. ..) whose particle displacements are symmetric about the neutral plane of the plate, and antisymmetric waves (Aq, A, . ..), whose displacements have odd symmetry about the neutral plane. Figure 3.38 shows that for sufficiently thin plates (M < 1-6), only two waves exist — the lowest-order symmetric mode (Sq) and the lowest-order antisymmetric mode (Aq). These are the modes shown earlier in Figure 2.0d. The plate mode that we will emphasize here is the Ao mode, in which the elements of the plate undergo flexure as the wave propagates. The shape of a plate during propagation of this flexural mode has been likened to that of a flag waving in the wind.

The distortion of the crystal is given by a transverse plane wave with the k vector perpendicular to the surface normal (thickness-shear mode). There are neither compressional waves [24] nor flexural contributions to the displacement pattern [46]. There are no nodal fines in the plane of the resonator. The standard model ignores anharmonic side bands (spurious modes) [23]. 

The deposition of noble metals onto oscillating quartz crystals of the thickness shear type, for fine adjustment of their frequency, has already been carried out for many years by frequency standard manufacturers. The idea of using the frequency decrease by mass deposition to determine the weight of the coating is comparatively new. Sauerbrey [35] and Lostis [36] were the first to propose the quartz-crystal microbalance. The AT-cut crystal oscillating in a thickness shear mode was found to be best suited for this purpose. The thickness xq of an infinite quartz plate is directly related to the wavelength A. of the continuous elastic transverse wave, the phase velocity vq of that wave and the frequency vq (i.e. the period xq) of the oscillating crystal, as shown in Fig. 4 ... 

Consider the web-flange splice shown in Figure 5.14. The fasteners are subjected to shear. Assume that the flange splice transfers the bending moment through tensile and compressive forces and that the web splice carries the transverse shear. The composite beams are made from fibre reinforced composite material. As the joint is loaded, the flanges and web move and the bolts contact portions of the holes. As the load is increased, failure of the joint may occur in different modes, i.e. net-section, bearing, and shear out. 

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