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The purpose of this paper is to investigate the effect of corrugation, wave number, initial stress and the heterogeneity of the media on the phase velocity of the Love-type wave. Moreover, the paper aims to have a comparative study of the presence and absence of anisotropy, heterogeneity, corrugation and initial stress in the half-space, which serve as a focal theme of the study.

The present paper modelled the propagation of the Love-type wave in a corrugated heterogeneous monoclinic layer lying over an initially stressed heterogeneous transversely isotropic half-space. The method of separation of variables is used to procure the dispersion relation.

The closed form of dispersion relation is obtained and found to be in well agreement to the classical Love wave equation. Neglecting the corrugation at either of the boundary surfaces, expressions of the phase velocity of the Love-type wave are deduced in closed form as special cases of the problem. It is established through the numerical computation of the obtained relation that the concerned affecting parameters have significant impact on the phase velocity of the Love-type wave. Also, a comparative study shows that the anisotropic case favours more to the phase velocity as comparison to the isotropic case.

Although many attempts have been made to study the effect of corrugated boundaries on reflection and refraction of seismic waves, but the effect of corrugated boundaries on the dispersion of surface wave (which are dispersive in nature) propagating through mediums pertaining various incredible features still needs to be investigated.

The purpose of this paper is to investigate the mathematical model comprising a heterogeneous fluid-saturated fissured porous layer overlying a non-homogeneous anisotropic fluid-saturated porous half-space without fissures. The influence of point source on horizontally polarized shear-wave (SH-wave) propagation has been studied intensely.

Techniques of Green’s function and Fourier transform are applied to acquire displacement components, and with the help of boundary conditions, complex frequency equation has been constructed.

Complex frequency relation leads to two distinct equations featuring dispersion and attenuation properties of SH-wave in a heterogeneous fissured porous medium. Using MATHEMATICA software, dispersion and damping curves are sketched to disclose the effects of heterogeneity parameters associated with both media, parameters related to rigidity and density of single porous half-space, attenuation coefficient, wave velocity, total porosity, volume fraction of fissures and anisotropy. The fact of obtaining classical Love wave equation by introducing several particular conditions establishes the validation of the considered model.

To the best of the authors’ knowledge, effect of point source on SH-wave propagating in porous layer containing macro as well as micro porosity is not analysed so far, although theory of fissured poroelasticity itself has vast applications in real life and impact of point source not only enhances the importance of fissured porous materials but also opens a new area for future research.

The purpose of this paper is to investigate the existence of SH-waves in fiber-reinforced layer placed over a heterogeneous elastic half-space.

The heterogeneity of the elastic half-space is caused by the exponential variations of density and rigidity. As a special case when both the layers are homogeneous, the derived equation is in agreement with the general equation of Love wave.

Numerically, it is observed that the velocity of SH-waves decreases with the increase of heterogeneity and reinforced parameters. The dimensionless phase velocity of SH-waves increases with the decreases of dimensionless wave number and shown through figures.

In this work, SH-wave in a fiber-reinforced anisotropic medium overlying a heterogeneous gravitational half-space has been investigated analytically and numerically. The dispersion equation for the propagation of SH-waves has been observed in terms of Whittaker function and its derivative of second degree order. It has been observed that on the removal of heterogeneity of half-space, and reinforced parameters of the layer, the derived dispersion equation reduces to Love wave dispersion equation thereby validates the solution of the problem. The equation of propagation of Love wave in fiber-reinforced medium over a heterogeneous half-space given by relevant authors is also reduced from the obtained dispersion relation under the considered geometry.

This paper aims to simplify a new frequency-independent model to calculate vertical vibration of rigid circular foundation resting on homogenous half-space and subjected to vertical harmonic excitation is presented in this paper.

The proposed model is an oscillator of single degree of freedom, which comprises a mass, a spring and a dashpot. In addition, a fictitious mass is added to the foundation. All coefficients are frequency-independent. The spring is equal to the static stiffness. Damping coefficient and fictitious mass are first calculated at resonance frequency where the response is maximal. Then, using a curve fitting technique the general formulas of damping and fictitious mass frequency-independent are established.

The validity of the proposed method is checked by comparing the predicted response with those obtained by the half-space theory. The dynamic responses of the new simplified model are also compared with those obtained by some existing lumped-parameter models.

Using this new method, to calculate the dynamic response of foundations, the engineer only needs the geometrical and mechanical characteristics of the foundation (mass and radius) and the soil (density, shear modulus and the Poisson’s ratio) using just a simple calculator. Impedance functions will no longer be needed in this new simplified method. The methodology used for the development of the new simplified model can be applied for the resolution of other problems in dynamics of soil and foundation (superficial and embedded foundations of arbitrary shape, other modes of vibration and foundations resting on non-homogeneous soil).

This paper aims to investigate the effects of inhomogeneities on the rolling contact fatigue (RCF) life in elastohydrodynamically lubricated (EHL) point contacts.

A numerical model for predicting the RCF life of inhomogeneous materials in EHL contacts was established by combining the EHL model and the inclusion model through the eigen-displacement and then connecting to the RCF life model through the subsurface stresses. Effects of the type, size, location and orientation of a single inhomogeneity and the distribution of multiple inhomogeneities on the RCF life were investigated.

The RCF life of a half-space containing manganese sulfide (MnS) inhomogeneity or the mixed inhomogeneity of aluminium oxide (Al₂O₃) and calcium oxide (CaO) was longer than that for the case of Al₂O₃ inhomogeneity. For a single ellipsoidal MnS inhomogeneity, increases of its semi-axis length and decreases of its horizontal distance between the inhomogeneity and the contact center shortened the RCF life. Furthermore, the relationship between the depth of a single MnS inhomogeneity and the RCF life was found. For the half-space containing multiple inhomogeneitites, the RCF life decreased remarkably compared with the homogeneous half-space and showed discreteness.

This paper implements the prediction of the RCF life of inhomogeneous materials under EHL condition.

The response of moving load over a surface is a subject of investigation because of its possible applications in determining the strength of a structure. Recently, with the enlargement of high-speed train networks, concern has been expressed about the effects of moving loads on the track, embankment and nearby structures. Earth surface and artificial structure are not always regular in nature. Irregularities are also responsible for structural collapse of long bridge and highway of plateau area under the action of moving loads. The purpose of this paper is to investigate the influence of irregularity on dynamic response due to a moving shear load.

At first the authors developed the mathematical model for the problem which is comprised of equation of motion together with boundary conditions. Perturbation technique has been used to derive the stresses produced in an irregular orthotropic half-space (which is influenced by gravity) due to a moving shear load. MATLAB and MATHEMATICA softwares have been employed for numerical computation as well as graphical illustration.

In this paper the authors have discussed the stresses produced in an irregular gravitating orthotropic half-space due to a moving shear load. The expression for shear stress has been established in closed form. Substantial effects of depth, irregularity factor, maximum depth of irregularity and gravitational parameter on shear stress have been reported. These effects are also exhibited by means of graphical illustration and numerical computation for an orthotropic material T300/5208 graphite/epoxy which is broadly used in aircraft designing. Moreover, comparison made through meticulous examination for different types of irregularity, presence and absence of anisotropy and gravity are highlighted.

A number of classical fatigue failures occur in aircraft structures. The moving load responsible for such fatigue failure may occur during manufacturing process, servicing, etc. Apart from these the aircraft structures may also experience load because of environmental damages (such as lightning strike, overheat) and mechanical damages (like impact damage, overload/bearing failure). Therefore the present study is likely to find application in the field of construction of highways, airport runways and earthquake engineering.

To the best of the authors’ knowledge no problem related to moving load on irregular orthotropic half-space under influence of gravity has been attempted by any author till date. Furthermore comparative study for different types of irregularity, presence and absence of anisotropy and influence of gravity on the dynamic response of moving load are novel and major highlights of the present study.

The purpose of this paper is to examine the dependency of dispersion and damping behavior of Love-type waves on wave number in a heterogeneous dry sandy double layer of finite thickness superimposed on heterogeneous viscoelastic substrate under the influence of hydrostatic initial stress.

The mechanical properties of the material of both the dry sandy layers vary with respect to a certain depth as quadratic and hyperbolic function, while it varies as an exponential function for the viscoelastic semi-infinite medium. The method of the separation of variables is employed to obtain the complex frequency equation.

The complex frequency equation is separated into real and imaginary components corresponding to dispersion and damping equation. After that, the obtained result coincides with the pre-established classical equation of Love wave, as shown in Section 5. The response of all mechanical parameters such as heterogeneities, sandiness, hydrostatic stress, thickness ratio, attenuation and viscoelasticity on both the phase and damped velocity against real wave number has been discussed with the help of numerical example and graphical demonstrations.

In this work, a comparative study clarifies that the Love wave propagates with higher speed in an isotropic elastic structure as compared to the proposed model. This study may find its applications in the investigation of mechanical behavior and deformation of the sedimentary rock.

The purpose of the current manuscript is to investigate the reflection of plane waves in a rotating, two-dimensional homogeneous, initially stressed, nonlocal orthotropic thermoelastic solid half-space based on dual-phase-lag model.

The reflection phenomenon has been utilized to study the effects of initial stress, rotation and nonlocal parameter on the amplitude ratios. During the reflection phenomenon three coupled waves, namely quasi displacement primary wave (qP), quasi thermal wave (qT) and quasi displacement secondary wave (qSV) have been observed in the medium, propagating with distinct velocities. After imposing the suitable boundary conditions, amplitude and energy ratios of the reflected waves are obtained in explicit form.

With the support of MATLAB programming, the amplitude ratios and energy ratios are plotted graphically to display the effects of rotation, initial stress and nonlocal parameters. Moreover, the impact of anisotropy and phase lags is also observed on the reflection coefficients of the propagating waves.

In the current work, we have considered rotation and nonlocality parameters in an initially stressed orthotropic thermoelastic half-space, which is lacking in the published literature in this field. The introduction of these parameters in a nonlocal orthotropic thermoelastic medium provides a more realistic model for these studies. The present work is valuable for the analysis of orthotropic thermoelastic problems involving rotation, initial stress and nonlocality parameters.

The two-dimensional deformation of a homogeneous, thermally conducting, monoclinic material has been studied by using Laplace and Fourier transforms technique. A linear temperature ramping function is used to more realistically model: thermal loading of the half-space surface. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating and loading. The displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and illustrated graphically. The comparison for Lord-Shulman (L-S), Green and Lindsay (G–L), Green and Naghdi (G–N) and Chandrasekharaiah and Tzou (CTU) theories have been shown graphically to estimate the effect of ramping parameter of heating for an insulated and temperature gradient boundaries.

The design of the study is eigenvalue approach

Homogeneous, thermally conducting monoclinic material has been taken under consideration to study the effect of linear temperature ramping parameter on temperature and normal displacement field. It is observed that magnitude of field quantities is large near the point of application of source for the non-dimensional values of time in all the four models. The numerical values for the field quantities are computed graphically for a wide range of values of finite pulse rise-time in the two situations t₀ < t, t₀ > t for generalized thermoelasticity theories.

(1) Governing equations for homogeneous, t₀ thermally conducting, monoclinic material are described and solved. (2) Eigen value approach is used to solve the problem. (3) The effect of ramping parameter of heating has been studied for various models of the thermoelasticity to show the comparision between them.

A newly developed frequency-independent lumped parameter model (LPM) is the purpose of the present paper. This new model’s direct outcome ensures high efficiency and a straightforward calculation of foundations’ vertical vibrations. A rigid circular foundation shape resting on a nonhomogeneous half-space subjected to a vertical time-harmonic excitation is considered.

A simple model representing the soil–foundation system consists of a single degree of freedom (SDOF) system incorporating a lumped mass linked to a frequency-independent spring and dashpot. Besides that, an additional fictitious mass is incorporated into the SDOF system. Several numerical methods and mathematical techniques are used to identify each SDOF’s parameter: (1) the vertical component of the static and dynamic foundation impedance function is calculated. This dynamic interaction problem is solved by using a formulation combining the boundary element method and the thin layer method, which allows the simulation of any complex nonhomogeneous half-space configuration. After, one determines the static stiffness’s expression of the circular foundation resting on a nonhomogeneous half-space. (2) The system’s parameters (dashpot coefficient and fictitious mass) are calculated at the resonance frequency; and (3) using a curve fitting technique, the general formulas of the frequency-independent dashpot coefficients and additional fictitious mass are established.

Comparisons with other results from a rigorous formulation were made to verify the developed model’s accuracy; these are exceptional cases of the more general problems that can be addressed (problems like shallow or embedded foundations of arbitrary shape, other vibration modes, etc.).

In this new LPM, the impedance functions will no longer be needed. The engineer only needs a limited number of input parameters (geometrical and mechanical characteristics of the foundation and the soil). Moreover, a simple calculator is required (i.e. we do not need any sophisticated software).