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.     

Reflection of plane waves at the free surface of a fibre-reinforced elastic half-space

The propagation of plane waves in fibre-reinforced, anisotropic, elastic media is discussed. The expressions for the phase velocity of quasi-P (qP) and quasi-SV (qSV) waves propagating in a plane containing the reinforcement direction are obtained as functions of the angle between the propagation and reinforcement directions. Closed form expressions for the amplitude ratios for qP and qSV waves reflected at the free surface of a fibre-reinforced, anisotropic, homogeneous, elastic half-space are obtained. These expressions are used to study the variation of amplitude ratios with angle of incidence. It is found that reinforcement has a significant effect on the amplitude ratios and critical angle     

Surface waves in fibre-reinforced anisotropic elastic media

The aim of this paper is to investigate surface waves in anisotropic fibre-reinforced solid elastic media. First, the theory of general surface waves has been derived and applied to study the particular cases of surface waves — Rayleigh, Love and Stoneley types. The wave velocity equations are found to be in agreement with the corresponding classical result when the anisotropic elastic parameters tends to zero. It is important to note that the Rayleigh type of wave velocity in the fibre-reinforced elastic medium increases to a considerable amount in comparison with the Rayleigh wave velocity in isotropic materials.     

Generation of SH-type waves in a poroelastic layer sandwiched between prestressed orthotropic and nonhomogeneous mantles

The present work is concerned with a detailed illustration on the study of horizontally polarized shear waves (SH-type) propagation in a prestressed fluid saturated anisotropic porous layer sandwiched by prestressed orthotropic medium and nonhomogeneous mantles. The frequency equation for the assumed model is derived and their medium characteristics, such as porosity, prestress, anisotropy, and nonhomogeneity, are discussed. Numerical treatment is given to analyze these effects on phase velocities of SH-type waves and is plotted in various graphs. The parametric study divulges that the magnitude of wave velocities increases with the increase of nonhomogeneity parameter and prestress parameter.     

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.     

Numerical modelling of the scattering of elastic waves in plates

This paper describes the application of finite difference methods to the calculation of the scattering of elastic waves. The emphasis is on cracklike defects in plates, and it is shown that a common numerical technique can span a range of wavelengths from Lamb waves to ultrasonic waves with many reflections from the surfaces of the plate. Quantitative results are given for the scattering of Lamb waves and ultrasonic shear waves from surface-breaking cracks.     

Nonlinear waves in a prestressed elastic tube filled with a layered fluid

In this work, we studied the propagation of weakly nonlinear waves in a prestressed thin elastic tube filled with an incompressible layered fluid, where the outer layer is assumed to be inviscid whereas the cylindrical core is considered to be viscous. Using the reductive perturbation technique, the propagation of weakly nonlinear waves in the longwave approximation is studied. The governing equation is shown to be the Korteweg-de Vries-Burgers' (KdV-B) equation. A travelling wave type of solution to this evolution equation is sought and it is observed that the formation of shock wave becomes evident with increasing core radius parameter.     

Shear stress distribution on a solid circular plate embedded in an elastic halfspace

The present investigation deals with the analysis of an axisymmetrically loaded elastic halfspace containing a solid circular plate. The elastic halfspace and the embedded plate has been idealised together as a layered system. Layered theory has been used to determine the shear stress distribution on the embedded plate. Results have been presented for the shear stress distribution on the embedded plate for different values of the relative rigidity parameter.     

Effects of inhomogeneity on surface waves in anisotropic media

This paper investigates the effects of anisotropy and inhomogeneity on surface waves in elastic media. Exponential variation in properties are assumed for the elastic parameters and material density. The classical equations of motion for propagation of waves in an inhomogeneous transversely isotropic elastic solid are deduced. The equations of motion for surface waves are derived and general surface waves are investigated. This general theory is then utilized to investigate Rayleigh, Love and Stoneley waves. Results obtained in the above cases reduce to the corresponding well-known classical results when inhomogeneity and anisotropy are not present. It is seen that inhomogeneity has significant effects on dispersion characteristics. Numerical calculations are included for Love waves and some conclusions have been drawn from the above calculations.     

Modulation of nonlinear waves in a viscous fluid contained in a tapered elastic tube

In the present work, treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube and the blood as a Newtonian fluid, we have studied the amplitude modulation of nonlinear waves in such a fluid-filled elastic tube, by use of the reductive perturbation method. The governing evolution equation is obtained as the dissipative nonlinear Schrödinger equation with variable coefficients. It is shown that this type of equations admit solitary wave solutions with variable wave amplitude and speed. It is observed that, the wave speed increases with distance for tubes of descending radius while it decreases for tubes of ascending radius. The dissipative effects cause a decay in wave amplitude and wave speed.     

Harmonic waves in a prestressed thin elastic tube filled with a viscous fluid

In this work a theoretical analysis is presented for wave propagation ina thin-walled prestressed elastic tube filled with a viscous fluid. Thefluid is assumed to be incompressible and Newtonian, whereas the tubematerial is considered to be incompressible, isotropic and elastic.Considering the physiological conditions that the arteries experience, sucha tube is initially subjected to a mean pressure P_i and anaxial stretch _z. If it is assumed that in the course ofblood flow small incremental disturbances are superimposed on this initialfield, then the governing equations of this incremental motion are obtainedfor the fluid and the elastic tube. A harmonic-wave type of solution issought for these field equations and the dispersion relation is obtained.Some special cases, as well as the general case, are discussed and thepresent formulation is compared with some previous works on the samesubject.     

Reflection of piezothermoelastic waves from the charge and stress free boundary of a transversely isotropic half space

The present paper concentrates on the study of propagation and reflection characteristics of waves from the stress free, thermally insulated/isothermal boundary of a piezothermoelastic half space. The non-classical (generalized) theories of linear piezo-thermoelasticity have been employed to investigate the problem. In the two-dimensional model of the transversely isotropic piezothermoelastic medium, there are three types of plane waves quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode), whose velocities depend on the angle of incidence and frequency. These waves are dispersive in character and are also affected by piezoelectric as well as pyroelectric properties of the materials. The low and high frequency approximations for the speeds of propagation and the attenuation coefficients of these waves have been obtained. The quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode) incident cases at the stress free, thermally insulated or isothermal open circuit boundary of a transversely isotropic piezothermoelastic half space are considered to discuss the reflection characteristics of various waves. The amplitude ratios of reflected waves to that of incident one in each case have been obtained. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection coefficients are carried out for cadmium Selenide (CdSe) material by using Gauss elimination procedure. In addition the phase velocities and attenuation coefficients are also computed along various directions of wave propagation. The obtained results in each case are presented graphically.     

Evolution equations for nonlinear waves in a tapered elastic tube filled with a viscous fluid

In this work, employing the reductive perturbation method and treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube, the propagation of weakly nonlinear waves is investigated in such a fluid-filled elastic tube. By considering the blood as an incompressible viscous fluid, depending on the viscosity and perturbation parameters we obtained various evolution equations as the extended Korteweg-de Vries (KdV), extended KdV Burgers and extended perturbed KdV equations. Progressive wave solutions to these evolution equations are obtained and it is observed that the wave speeds increase with the distance for negative tapering while they decrease for positive tapering.     

Effect of voids on the propagation of waves in an elastic layer

The present paper investigates the propagation of waves in an elastic layer containing voids. Numerical calculations and discussions indicate that the velocity of the propagation of waves decreases due to the presence of voids in the material medium of the layer and the voids cause dispersion of the general waveform.     

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.     

Rayleigh-Lamb waves in magneto-thermoelastic homogeneous isotropic plate

The propagation of magnetic-thermoelastic plane wave in an initially unstressed, homogeneous isotropic, conducting plate under uniform static magnetic field has been investigated. The generalized theory of thermoelasticity is employed, by assuming electrical behaviour as quasi-static and the mechanical behaviour as dynamic, to study the problem. The secular equations for both symmetric and skew-symmetric waves have been obtained. The magneto-elastic shear horizontal (SH) mode of wave propagation gets decoupled from rest of the motion and it is not influenced by thermal variations and thermal relaxation times. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to Rayleigh surface wave frequency equation, because a finite thickness plate in such a situation behaves like a semi-infinite medium. Thin plate results are also deduced at the end. Dispersion curves are represented graphically for various modes of wave propagation in different theories of thermoelasticity. The amplitudes of displacement, perturbed magnetic field and temperature change are also obtained analytically and computed numerically. The result in case of elastokinetics, magneto-elasticity and coupled magneto-elasticity has also been deduced as special cases at appropriate stages of this work.     

Propagation of Love waves in an elastic layer with void pores

The paper presents a study of propagation of Love waves in a poroelastic layer resting over a poro-elastic half-space. Pores contain nothing of mechanical or energetic significance. The study reveals that such a medium transmits two types of love waves. The first front depends upon the modulus of rigidity of the elastic matrix of the medium and is the same as the love wave in an elastic layer over an elastic half-space. The second front depends upon the change in volume fraction of the pores. As the first front is well-known, the second front has been investigated numerically for different values of void parameters. It is observed that the second front is many times faster than the shear wave in the void medium due to change in volume fraction of the pores and is significant     

Effect of surface stresses on surface waves in elastic solids

This paper deals with the propagation of surface waves in homogeneous, elastic solid media whose free surfaces or interfaces of separation are capable of supporting their own stress fields. The general theory for the propagation of surface waves in a medium which supports surface stresses is first deduced, and then this theory is employed to investigate the particular cases of surface waves, viz. (a) Rayleigh waves, (b) Love waves and (c) Stoneley waves. It is seen that the Rayleigh waves become dispersive in nature; and, in case of low frequency with residual surface tension, a critical wavelength exists, below which the propagation of Rayleigh waves is not possible. This critical wave length is directly proportional to the surface tension. Some numerical calculations have been made in the case of Love waves and conclusions have been drawn.     

Shear flow over a particulate or fibrous plate

Simple shear flow over a porous plate consisting of a planar array of particles is studied as a model of flow over a membrane. The main objective is to compute the slip velocity defined with reference to the velocity profile far above the plate, and the drift velocity induced by the shear flow underneath the plate. The difference between these two velocities is shown to be proportional to the thickness of the plate. When the geometry of the particle array is anisotropic, the directions of the slip and drift velocity are generally different from the direction of the overpassing shear flow. An integral formulation is developed to describe flow over a plate consisting of a periodic lattice of particles with arbitrary shape, and integral representations for the velocity and pressure are developed in terms of the doubly-periodic Green's function of three-dimensional Stokes flow. Based on the integral representation, asymptotic expressions for the slip and drift velocity are derived to describe the limit where the particle size is small compared to the inter-particle separation, and numerical results are presented for spherical and spheroidal particles of arbitrary size. The asymptotic results are found to be accurate over an extended range of particle sizes. To study the limit of small plate porosity, the available solution for shear flow over a plane wall with a circular orifice is used to describe flow over a plate with a homogeneous distribution of circular perforations, and expressions for the slip and drift velocity are derived. Corresponding results are presented for axial and transverse shear now over a periodic array of cylinders arranged distributed in a plane. Streamline pattern illustrations confirm that a negative drift velocity is due to the onset of eddies between closely-spaced particles.