Viscoelastic properties wave equation

Mason [46] first observed that the viscoelastic properties of a fluid in contact with quartz crystals can affect the resonant properties. However, Mason s work had been forgotten and for a long time there have not been studies of piezoelectric acoustic wave devices in contact with liquids until Nomura and Okuhara [15] found an empirical expression that described the changes in the quartz resonant frequency as a function of the liquid density, its viscosity and the conductivity in which the crystal was immersed. Shortly after the empirical observations of Nomura were described in terms of physical models by Kanazawa [1] and Bruckenstein [2] who derived the equation that describes the changes in resonant frequency of a loss-less quartz crystal in contact with an infinite, non conductive and perfectly Newtonian fluid ... 

Analysis of these effects is difficult and time consuming. Much recent work has utilized two-dimensional, finite-difference computer codes which require as input extensive material properties, e.g., yield and failure criteria, and constitutive laws. These codes solve the equations of motion for boundary conditions corresponding to given impact geometry and velocities. They have been widely and successfully used to predict the response of metals to high rate impact (2), but extension of this technique to polymeric materials has not been totally successful, partly because of the necessity to incorporate rate effects into the material properties. In this work we examined the strain rate and temperature sensitivity of the yield and fracture behavior of a series of rubber-modified acrylic materials. These materials have commercial and military importance for impact protection since as much as a twofold improvement in high rate impact resistance can be achieved with the proper rubber content. The objective of the study was to develop rate-sensitive yield and failure criteria in a form which could be incorporated into the computer codes. Other material properties (such as the influence of a hydrostatic pressure component on yield and failure and the relaxation spectra necessary to define viscoelastic wave propagation) are necssary before the material description is complete, but these areas will be left for later papers. 

The coated material used on the pipe is usually a viscoelastic layer adhered on the pipe. The internal losses in the coated material are modeled according to the theory of linear viscoelasticity, which is also the model implemented in the software DISPERSE [17] used for the wave structure analysis. The shear velocity and shear attenuation of bitumen are obtained from the result of Simonetti measurement [16] for the software used to predict the attenuation of guided wave. The material properties of the other two coated materials are found from the data bank in the DISPERSE software. The theory of linear viscoelasticity for isotropic and homogenous media is modeled in the frequency domain, which leads to linear equation of motion [18]. Thus... 

The detection of gas analytes using acoustic wave (AW) sensors can be based on changes in one or more of the physical characteristics of a thin film or layer in contact with the device surface (Ballantine et al. 1997). Some of the intrinsic film properties that can be utilized for gas detection include mass/ area, elastic stiffness (modulus), viscoelasticity, viscosity, electrical conductivity, and permittivity. Variations in any of these parameters alter the mechanical and/or electrical boundary conditions producing a measurable shift in the propagating acoustic wave phase velocity, v . Equation (13.1) illustrates the change in acoustic phase velocity, Av, as a result of external perturbations, assuming that the perturbations are small and linearly combined (Ippolito et al. 2009) ... 

---