Shear wave propagation in viscoelastic heterogeneous layers lying over an initially stressed half-space

The role of the present article is to study the propagation of horizontally polarized shear waves in vertically heterogeneous viscoelastic double layers lying over a homogeneous half-space under initial stress. Both linear and exponential variations have been considered in the inhomogeneity associated to rigidity, internal friction, and density of the media. The dispersion equation of shear waves has been obtained in closed form. The dimensionless phase and damping velocities have been plotted against dimensionless wave number for different values of inhomogeneity parameters separately. Also, surface plots of phase velocity against dimensionless wave number and inhomogeneity parameters have been given.     

Surface wave propagation in a double liquid layer over a liquid-saturated porous half-space

The frequency equation is derived for surface waves in a liquid-saturated porous half-space supporting a double layer, that of inhomogeneous and homogeneous liquids. Asymptotic approximations of Bessel functions are used for long and short wavelength cases. Certain other problems are discussed as special cases. Velocity ratio (phase and group velocity) is obtained as a function of wavenumber and the results are shown graphically.     

Reflection of plane micropolar viscoelastic waves at a loosely bonded solid-solid interface

A solution of the field equations governing small motions of a micropolar viscoelastic solid half-space is employed to study the reflection and transmission of plane waves at a loosely bonded interface between two dissimilar micropolar viscoelastic solid half-spaces. The amplitude ratios for various reflected and refracted waves are computed for a particular model for different values of bonding parameter. The variations of these amplitude ratios with the angle of incidence are shown graphically. Effects of bonding parameter and viscosity on the amplitude ratios are shown.     

Effect of fluid viscosity on wave propagation in a cylindrical bore in micropolar elastic medium

Wave propagation in a cylindrical bore filled with viscous liquid and situated in a micropolar elastic medium of infinite extent is studied. Frequency equation for surface wave propagation near the surface of the cylindrical bore is obtained and the effect of viscosity and micropolarity on dispersion curves is observed. The earlier problems of Biot and of Banerji and Sengupta have been reduced as a special case of our problem.     

Rayleigh wave propagation in a viscoelastic half-space

Summary Rayleigh waves excited by an impulsive force imbedded in a linear viscoelastic half-space are synthesized by applying an approximate inversion of the Fourier transform which yields reliable results. The method is general enough and can be applied to general models of viscoelasticity described by the Boltzmann superposition principle, with a relaxation or creep function given analytically or numerically in the time or frequency domain. Illustrations are given in cases of simple and complicated models of viscoelasticity.     

Reflection and transmission of plane harmonic waves at an interface between liquid and micropolar viscoelastic solid with stretch

A solution of the field equations governing small motions of a micropolar viscoelastic solid half-space with stretch is employed to study the reflection and transmission at the interface between a liquid and a micropolar viscoelastic solid with stretch. The amplitude ratios for various reflected and refracted waves are computed and depicted graphically. Effects of axial stretch and viscosity on the amplitude ratios are discussed     

On wave propagation in a micropolar elastic cylinder

An asymptotic analysis of the free vibrations of a micropolar elastic cylinder is earned out postulating the displacements, the micro-rotations and the frequency as power series in the nondimensional $\text{? = 2π}\text{radius/(wave length)}$.     

Two-dimensional wave propagation in a micropolar thermo-elastic layer

The object of the present paper is to investigate the 2-dimensional thermo-elastic wave propagation in a micropolar solid layer. The wave velocity equation for the thermo-elastic Rayleigh wave in the micropolar medium has been deduced from the above theory and in the limiting case the wave velocity equation so obtained is in agreement with the corresponding classical problem when the thermal and micropolar effects are vanishingly small.     

Shear waves in magneto-elastic transversely isotropic (MTI) layer bonded between two heterogeneous elastic media

This paper studies shear wave propagation in magneto-elastic transversely isotropic material, sandwiched between a layer and a half-space of heterogeneous elastic materials. Elastic constants of the layer and half-space are assumed to vary in a parabolic form with depth. Whittaker’s functions and variable separable techniques have been employed to calculate the interior deformations; consequently, we obtain a general dispersion relation for shear wave. Effects of various affecting parameters on phase velocity of shear wave are considered through some numerical examples. In addition, a comparative study has been carried out for three examples of sandwiched layer, namely Beryl, Magnesium and isotropic.     

Rayleigh wave propagation in a solid with a cold-worked surface layer

The propagation of the Rayleigh surface wave is experimentally studied along the top surface of used railroad rail under conditions where ultrasonic pulses have carrier frequencies ranging from 0.4 to 3.0 MHz and approximately 10 µs duration. The generation of the first higher (M ₂₁ or Sezawa) mode as well as the fundamental (M ₁₁) mode and their dispersion properties are observed. These phenomena are attributable to the presence of the cold-worked surface layer caused by the wheel passage. It is shown that a theoretical model of a single layer overlying a half space, whose elastic constants are determined by a destructive method, yields results which agree with the dispersion curves obtained experimentally. On the basis of this one-layered model, an inversion method to estimate the layer thickness and its elastic constants is discussed.     

Love wave propagation in a solid with a cold-worked surface layer

In this paper, experiments show Love wave generation along the top surface of used railroad rail, where the shear wave velocity has been slightly reduced by the cold-working of wheel passage for years. The rf pulses used in the experiments have about 10 µs duration and a relatively narrow frequency spectrum. The group velocity of the Love wave is found to have a strong dependence on the carrier frequency over the tested range of 0.45–3.1 MHz. Application of the seismological one-layered model to the experimental measurements yields an NDE technique for the elastic properties and the thickness of the cold-worked surface layer. The results are interpreted on the basis of a destructive observation by micro-Vickers hardness testing.     

Two-dimensional wave propagation in a micropolar thermo-elastic layer with stretch

This paper deals with the propagation of 2-dimensional waves in a thermo-elastic micropolar solid layer which can stretch and contract. Thermo-elastic Rayleigh wave velocity equation in the micropolar medium with stretch has been deduced from the above theory. The wave velocity equation obtained is in agreement with the classical result of Rayleigh when the layer is unstretched and thermal and micropolar effects are negligibly small.     

Surface wave propagation in sandy layer overlying a liquid saturated porous half-space and lying under a uniform liquid layer

Dispersion of Rayleigh-type surface waves is studied in a sandy layer under a uniform layer of homogeneous liquid lying over liquid-saturated porous solid half-space. The frequency equation in the form of a ninth-order determinant is obtained and evaluated. Special cases have been deduced and dispersion curves for the phase velocity and wave number have been plotted for a particular model.     

Electromagnetic effects on Rayleigh surface wave propagation in a homogeneous isotropic thermo-microstretch elastic half-space

This paper deals with the problem of electromagnetic effect on the propagation of Rayleigh surface waves in a homogeneous, isotropic, thermally-conducting microstretch elastic half-space. In this context, the generalized theory of thermoelasticity is considered. The governing equations for the Rayleigh surface waves in the cases of insulated as well as isothermal boundaries are derived. In the presence of the magnetic effect, the analytical expressions for the displacement, microrotation, microstretch, and temperature changes are obtained. The changes in the phase velocity, microrotation, and path of particles for aluminum epoxy material are presented graphically.     

Guided wave propagation in an elastic hollow cylinder coated with a viscoelastic material

The propagation of ultrasonic guided waves in an elastic hollow cylinder with a viscoelastic coating is studied. The principle motivation is to provide tools for performing a guided wave, nondestructive inspection of piping and tubing with viscoelastic coatings. The theoretical boundary value problem is solved that describes the guided wave propagation in these structures for the purpose of finding the guided wave modes that propagate with little or no attenuation. The model uses the global matrix technique to generate the dispersion equation for the longitudinal modes of a system of an arbitrary number of perfectly bonded hollow cylinders with traction-free outer surfaces. A numerical solution of the dispersion equation produces the phase velocity and attenuation dispersion curves that describe the nature of the guided wave propagation. The attenuation dispersion curves show some guided wave modes that propagate with little or no attenuation in the coated structures of interest. The wave structure is examined for two of the modes to verify that the boundary conditions are satisfied and to explain their attenuation behavior. Experimental results are produced using an array of transducers positioned circumferentially around the pipe to evaluate the accuracy of the numerical solution.     

Dispersion of suspended particles in a wave boundary layer over a viscoelastic bed

This is an analytical study with an aim to show the effects of a viscoelastic muddy bottom on the wave-induced convection and dispersion of a dilute suspension in the wave boundary layer above the viscoelastic bottom. It is shown that, depending on the rheology of the mud, the convection velocity and dispersion coefficient are non-monotonic functions of the thickness of the mud layer. When the elasticity dominates, appreciable resonant amplification of the mud motion can happen to a layer of certain thickness, which may lead to an order of magnitude increase in the dispersion coefficient and a negative convection velocity as well. It is, however, also possible that, away from these resonant mud depths, the convection velocity and dispersion coefficient are diminished, even to the extent to become virtually zero. All these transport phenomena are related to the oscillatory movement of the water-mud interface, in terms of phase and amplitude, relative to the movement of the near-bottom water particles.     

Dynamic steady-state crack propagation in a transversely isotropic viscoelastic body

The problem considered herein is the dynamic, subsonic, steady-state propagation of a semi-infinite, generalized plane strain crack in an infinite, transversely isotropic, linear viscoelastic body. The corresponding boundary value problem is considered initially for a general anisotropic, linear viscoelastic body and reduced via transform methods to a matrix Riemann–Hilbert problem. The general problem does not readily yield explicit closed form solutions, so attention is addressed to the special case of a transversely isotropic viscoelastic body whose principal axis of material symmetry is parallel to the crack edge. For this special case, the out-of-plane shear (Mode III), in-plane shear (Mode II) and in-plane opening (Mode I) modes uncouple. Explicit expressions are then constructed for all three Stress Intensity Factors (SIF). The analysis is valid for quite general forms for the relevant viscoelastic relaxation functions subject only to the thermodynamic restriction that work done in closed cycles be non-negative. As a special case, an analytical solution of the Mode I problem for a general isotropic linear viscoelastic material is obtained without the usual assumption of a constant Poissons ratio or exponential decay of the bulk and shear relaxation functions. The Mode I SIF is then calculated for a generalized standard linear solid with unequal mean relaxation times in bulk and shear leading to a non-constant Poissons ratio. Numerical simulations are performed for both point loading on the crack faces and for a uniform traction applied to a compact portion of the crack faces. In both cases, it is observed that the SIF can vanish for crack speeds well below the glassy Rayleigh wave speed. This phenomenon is not seen for Mode I cracks in elastic material or for Mode III cracks in viscoelastic material.     

Anti-symmetric motion of a pre-stressed incompressible elastic layer near shear resonance

A two-dimensional model is derived for anti-symmetric motion in the vicinity of the shear resonance frequencies in a pre-stressed incompressible elastic plate. The method of asymptotic integration is used and a second-order solution, for infinitesimal displacement components and incremental pressure, is obtained in terms of the long-wave amplitude. The leading-order hyperbolic governing equation for the long-wave amplitude is observed to be not wave-like for certain pre-stressed states, with time and one of the in-plane spatial variables swapping roles. This phenomenon is shown to be intimately related to the possible existence of negative group velocity at low wave number, i.e. in the vicinity of shear resonance frequencies.