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.     

狭缝空腔间粘弹性体中弹性波传播特性的研究

利用笛卡尔坐标下的Kelvin-Voigt线性粘弹性模型,研究了无限长粘弹性狭缝通道中波的传播和衰减。利用自适应绕数求根方法,针对具有狭缝形空腔周期性分布覆盖层的吸声问题,求得频散方程的根,并且得到无限长狭缝空腔中相速度频散曲线和衰减曲线。分析了各阶模式对无限长粘弹性狭缝结构中波传播的相速度和衰减的影响。通过引入复粘弹性模量,粘弹性波动方程具有弹性波动方程相对应的形式,计算中可用复值粘弹性模量代替相应的弹性模量。粘弹性狭缝结构中所有波传播模式均存在衰减,高阶波在某个频率以下衰减非常大,而在该频率以上逐渐减小;最低阶模式的相速度与材料无损耗的情况非常接近。粘弹性狭缝结构中波传播的衰减特性不仅与狭缝的结构参数有关,还与粘弹性材料本身的复弹性模量有关。     

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.     

Rayleigh-type wave propagation on a transversely isotropic viscoelastic layer with yielding and rigid foundations

The present study investigates the propagation of Rayleigh-type wave in a transversely isotropic viscoelastic layer in effect of yielding foundation and rigid foundation in two different cases for two considered models. Numerical computation and graphical demonstration have been carried out for the case when layer is comprised of transversely isotropic viscoelastic Mesaverde clay shale material (Model I) and simply isotropic viscoelastic material (Model II). Closed-form expression of phase velocity and damped velocity for both the cases are deduced analytically. Obtained result is found in well agreement to the established standard results existing in the literature. Significant effect of dilatational viscoelasticity, volume viscoelasticity and yielding parameter on phase and damped velocities for both the considered models has been traced out. The comparative study has been performed to unravel the effect of viscoelasticity over elasticity and anisotropy over isotropy in the context of the present problem. Moreover, comparison of phase and damped velocities for the case of layer with stress-free foundation, layer with rigid foundation and layer with yielding foundation serve as a major highlight of the present work.     

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.     

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.     

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.     

Studying nonlinear thermomechanical wave propagation in a viscoelastic layer based upon the Lord-Shulman theory

Abstract

Based on the Lord–Shulman (L-S) theory, the thermally nonlinear coupled thermo-viscoelasticity of a layer is analyzed using a numerical approach. Using the Kelvin-Voigt theory of viscoelasticity in conjunction with the L-S theory, the coupled governing equations are first derived in variational form. Then, the variational differential quadrature (VDQ) method is applied to solve the problem numerically. Parametric studies are presented in order to reveal the effects of viscoelastic parameter, intensity of heat flux and relaxation time on the propagation of displacement, temperature and stress waves. Furthermore, the influence of considering nonlinearity in the energy equation is analyzed.     

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.     

A simple multi‐directional absorbing layer method to simulate elastic wave propagation in unbounded domains

The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or layered solids. Various techniques such as Absorbing Boundary Conditions, infinite elements or Absorbing Boundary Layers (e.g. Perfectly Matched Layers) lead to an important reduction of such spurious reflections. In this paper, a simple absorbing layer method is proposed: it is based on a Rayleigh/Caughey damping formulation which is often already available in existing Finite Element softwares. The principle of the Caughey Absorbing Layer Method is first presented (including a rheological interpretation). The efficiency of the method is then shown through 1D Finite Element simulations considering homogeneous and heterogeneous damping in the absorbing layer. 2D models are considered afterwards to assess the efficiency of the absorbing layer method for various wave types and incidences. A comparison with the PML method is first performed for pure P‐waves and the method is shown to be reliable in a more complex 2D case involving various wave types and incidences. It may thus be used for various types of problems involving elastic waves (e.g. machine vibrations, seismic waves, etc.). Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

On waves in a random micropolar conducting magneto-thermo-viscoelastic medium

Effects of random inhomogeneity on wave propagation in the interacting micropolar conducting magneto-generalized thermo-viscoelastic medium are studied. The couple stress theory relevant to micropolar solids is employed. The analysis is carried out under the smooth perturbation technique amenable to stochastic linear differential equations up to the second perturbation. The perturbing field has been assumed to be weakly conducting and weakly thermal. The generalized thermoelasticity has been used. Six different types of waves have been observed to propagate in the medium. The dispersion equations have been derived. Effects due to random variations of micropolar-elastic, conducting-electromagnetic and generalized thermo-visco-parameters have been computed. Effects of random heterogeneity of the conducting magnetic field are readily available up to first order perturbation. However effects of the generalized thermal field are discernible only in the domain of second order perturbation. Change of phase speed occurs on account of randomness. Attenuation coefficients for types of waves have been computed. A special type of generalized theromomechanical auto- and cross-correlation functions has been used to approximately measure effects of random variations of parameters. Uncoupled problem has been formulated for future investigations.     

The partition of unity finite element method for elastic wave propagation in Reissner–Mindlin plates

This paper reports a numerical method for modelling the elastic wave propagation in plates. The method is based on the partition of unity approach, in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment. The technique is general, such that it can be applied to the Lagrangian family of finite elements with specific waveform enrichment schemes, depending on the dominant modes of wave propagation in the physical system. A four‐noded element for the Reissner–Mindlin plate is derived in this paper, which is free of shear locking. Such a locking‐free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain. As a result, the frequency‐dependent stiffness matrix and the mass matrix are obtained, which capture the higher frequency response with even coarse meshes, accurately. The steps involved in the numerical implementation of such element are discussed in details. Numerical studies on the performance of the proposed element are reported by considering a number of cases, which show very good accuracy and low computational cost. Copyright © 2006 John Wiley & Sons, Ltd.