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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 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 research is to study the reflection and refraction of elastic waves at the interface of an elastic half‐space and initially stressed thermoelastic with voids half‐space.

A two‐dimensional model was considered of an isotropic elastic half‐space (medium I) lying over a homogeneous isotropic generalized initially stressed thermoelastic with voids half‐space(medium II). There exist two waves, P‐wave and SV‐wave in isotropic elastic half‐space and three quasi‐longitudinal waves namely, quasi‐longitudinal wave (QP‐mode), quasi‐longitudinal thermal wave (QPT‐mode), quasi‐longitudinal volume fractional wave (QPV‐mode) and one quasi‐transverse wave (QSV‐mode) exists in initially stressed thermoelastic with voids half‐space.

The energy ratios of these waves are computed along various directions of incident wave, and it is found that the sum of all energy ratios is exactly unity at each value of incident angle. The amplitude ratios of various waves were obtained numerically.

Reflection and refraction of an elastic medium is of great practical importance. Since valuable organic and inorganic deposits beneath the earth surface are difficult to detect by drilling randomly, wave propagation is the simplest and most economic technique to these and does not require any drilling through the earth. Almost all the oil companies rely on seismic interpretation for selecting the sites for exploratory oil wells because seismic wave methods have higher accuracy, higher resolution and more economical, as compared to drilling which is expansive and time consuming.

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.

The purpose of this paper is to investigate the effect of initial stress and heterogeneity on the propagation of torsional waves in dissipative medium. The problem consists of dry sand poroelastic half-space embedded between heterogeneous self-reinforced half-space and poroelastic medium. The frequency equation is derived in the framework of Biot's theory with some variants.

Torsional wave propagation in dry sand poroelastic half-space embedded between self-reinforced half-space and poroelastic medium. All the constituents here are assumed to be dissipative, heterogeneous and initial stressed.

Phase velocity and attenuation are computed against wavenumber for various values of self-reinforcement parameter, inhomogeneity parameter and initial stress. Particular cases are discussed in absence of dissipation. The numerical results are presented graphically.

Initial stress and heterogeneity effects on torsional waves in dry sand half-space between reinforced half-space and poroelastic medium are investigated. The frequency equation is derived, and which intern gives the phase velocity and attenuation coefficient for various values of initial stress, self-reinforcement parameter and heterogeneity parameter. From the numerical results, it is clear that as wavenumber varies phase velocity and attenuation are periodic in nature for all the cases. Particular cases are discussed in absence of dissipation. This kind of analysis can be extended to any elastic solid by taking magnetic, thermo and piezoelectric effects into account.

The purpose of this research is to study the reflection and transmission of elastic waves at the interface of an elastic half‐space and initially stressed thermoelastic diffusion with voids half‐space.

Two‐dimensional model has been considered of an isotropic elastic half‐space (Medium I) lying over a homogeneous isotropic generalized initially stressed thermoelastic diffusion with voids half‐space (Medium II). There exist two waves, P‐wave and SV‐wave, in isotropic elastic half‐space and four quasi‐longitudinal waves, namely, quasi‐longitudinal wave (QP‐mode), quasi‐longitudinal mass diffusive wave (QMD‐mode), quasi‐longitudinal thermal wave (QPT‐mode) and quasi‐longitudinal volume fractional wave (QPV‐mode), and one quasi‐transverse wave (QSV‐mode) exists in initially stressed thermoelastic diffusion with voids half‐space.

The energy ratios of these waves are computed along various directions of incident wave, and it is found that the sum of all energy ratios is exactly unity at each value of incident angle. The amplitude ratios of various waves have been obtained numerically.

Reflection and transmission of an elastic medium is of great practical importance. Since valuable organic and inorganic deposits beneath the earth surface are difficult to detect by drilling randomly, wave propagation is the simplest and most economic technique for these and does not require any drilling through the earth. Almost all the oil companies rely on seismic interpretation for selecting the sites for exploratory oil wells because seismic wave methods have higher accuracy, have higher resolution and are more economical, as compared to drilling which is expansive and time consuming.

The purpose of this paper is to investigate the effect of reinforcement, inhomogeneity and initial stress on the propagation of shear waves. The problem consists of magneto poroelastic medium sandwiched between self-reinforced medium and poroelastic half space. Using Biot’s theory of wave propagation, the frequency equation is obtained.

Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium and poroelastic half space is investigated. This particular setup is quite possible in the Earth crust. All the three media are assumed to be inhomogeneous under initial stress. The significant effects of initial stress and inhomogeneity parameters of individual media have been studied.

Phase velocity is computed against wavenumber for various values of self-reinforcement, heterogeneity parameter and initial stress. Classical elasticity results are deduced as a particular case of the present study. Also in the absence of inhomogeneity and initial stress, frequency equation is discussed. Graphical representation is made to exhibit the results.

Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium, and poroelastic half space are investigated in presence of initial stress, and inhomogeneity parameter. For heterogeneous poroelastic half space, the Whittaker’s solution is obtained. From the numerical results, it is observed that heterogeneity parameter, inhomogeneity parameter and reinforcement parameter have significant influences on the wave characteristics. In addition, frequency equation is discussed in absence of inhomogeneity and initial stress. For the validation purpose, numerical results are also computed for a particular case.

The purpose of this study is stated regarding the impact of the horizontally polarized shear wave vibration on a composite medium in the terms of phase and damped velocity.

The assumed composite is composed of magneto-elastic fiber-reinforced (MEFR) layer constrained between heterogeneous viscoelastic layer and heterogeneous elastic half-space. The considered heterogeneity is associated with the directional rigidity and mass density in the uppermost layer and half-space of quadratic and trigonometric types, respectively. The coupled field equations related to the respective medium are solved analytically by employing the method of separation of variables.

The dispersion relation of the stated problem is secured by using the continuity assumptions, imposed at the stress-free surface and the interfaces of the expressed medium. The adopted numerical examples are used to compute the dispersion relation and plot the graphs between phase/damped velocity and wave number. Parametric studies on the phase and damped velocity yield five main conclusions: (1) Phase velocity decreases with increasing value of wave number and damped velocity increases up to a certain number and then starts falling simultaneously with increasing magnitude of wave number while keeping the rest parametric values fixed. (2) The presence of heterogeneity in the upper layer enhances the phase velocity and diminishes the damped velocity, but the presence of heterogeneity in the half-space enhances both the phase and damped velocity. (3) The appearance of reinforced parameters enhances the phase velocity for the considered crystalline graphite material and diminishes the phase velocity for the rest materials (carbon fiber-epoxy resin and steel) of the MEFR layer. Similarly, damped velocity decreases for the assumed crystalline graphite material of the MEFR layer and increases for the rest materials of the MEFR layer. (4) The induced dissipation factor due to viscoelastic property shows reversal decreasing and increasing effect on phase and damped velocity of SH-wave. (5) Ascending values of the angle at which the wave crosses the magnetic field increase the phase velocity and decrease the damped velocity for all the considered MEFR examples.

Till date, the mathematical modeling as well as vibrational analysis of wave propagation through the composite structure consisting of MEFR layer constrained between viscoelastic media and elastic half-space under the effect of different varying properties with depth remains a new challenging issue for the researchers around the globe. The current analysis is an approach to move ahead in the era of wave propagation in different realistic models based on their parametric studies. Also, these studies are very helpful to find their applications in the field of mechanical, construction, aerospace, automobile, biomedical, marine, manufacturing industries and many branches of science and technology where magnetic fields induced in elastic deformation occur.

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).

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.