Incident qP Research Articles

On reflection and transmission of qP waves in initially stressed viscoelastic triclinic layer between distinct triclinic geomedia with sliding interface

The present study dwells with the propagation of quasi seismic qP waves in an initially stressed highly anisotropic viscoelastic triclinic layer which is in sliding contact with the upper initially stressed viscoelastic triclinic half-space. The propagation characteristics of all the reflected/transmitted wave generated by the incident qP wave through initially stressed viscoelastic triclinic substratum have been analysed in detail. Closed-form analytical expressions for reflection/transmission (RT) angles, velocity and coefficients of all the propagating waves have been derived. Effects of incident angle, layer width, initial stress and sliding parameter have been analysed and shown graphically. The energy ratio and slowness diagram have also been calculated and depicted graphically. Particular cases of free and fixed welded interface are analysed and drawn for validating the results of numerical simulation. Present work may be useful in domain with highly anisotropic viscoelastic geomedia equipped with initial stress and imperfect bonding between different interfaces such as transform-fault boundary.

Analysis of plane wave reflection phenomenon from the surface of a micro-mechanically modeled piezomagnetic fiber-reinforced composite half-space

In the present article, firstly, the micro-mechanical model of piezomagnetic fiber-reinforced composite (PMFRC), composed of CoFeO fiber-epoxy matrix combination, is presented employing the Strength of Materials (SM) and Rule of Mixtures (RM) techniques. Secondly, the impacts of varying fiber-volume fractions () on the energies carried by different reflected waves in the PMFRC are analytically studied. Due to the incidence of a quasi-longitudinal wave, three reflected waves viz. quasi-longitudinal (qP), quasi-transverse (qSV), and magneto-acoustic (MA) waves are generated in the PMFRC half-space. Propagation angles of all reflected waves are analyzed considering incident qP and qSV waves, and the existence of critical angles is established for the latter case. The closed-form expressions of amplitude ratios of all reflected waves are derived by employing appropriate magneto-mechanical boundary conditions and using Cramer's rule. In order to validate the numerical results, the expressions of energy ratios of all reflected waves and interaction energy are derived, which exhibit the influence of existing parameters. In doing so, the Law of Conservation of Energy is also established. The existence of a critical value of is discovered in the range , beyond which the magnitudes of energies carried by the reflected waves change drastically.

Three-Dimensional Dynamic Response Analysis of Rigid Foundation Embedded in Layered Transversely Isotropic Half-Space

ABSTRACT This paper employs an indirect boundary element formulation for 3D soil-structure interaction analysis in layered transversely isotropic (TI) elastic half-space under incident qP, qSV, and SH waves. Transformation matrix and dynamic Green’s function are employed to compute dynamic impedance coefficients, and foundation displacement is computed by superposition of two cases (with and without mass of foundation and upper structure). Upper structure displacement is solved from dynamic equilibrium equation. An embedded foundation with a single-point structure is simulated to study the influence of the ratio of transverse and vertical Young’s modulus of TI medium and incident angle on soil-structure system response.

A 2.5D IBEM to investigate the 3D seismic response of 2D topographies in a multi-layered transversely isotropic half-space

A two and half dimensional (2.5D) indirect boundary element method (IBEM) is developed to study the three dimensional (3D) seismic response of two dimensional (2D) topographies in a multi-layered transversely isotropic (TI) half-space, under obliquely incident qP-, qSV- and SH-waves. Based on the single-layer integral representation, the scattered fields are constructed by applying fictitious moving load on the boundary line elements, and the load densities are determined from the corresponding boundary conditions. The total wave fields can be obtained by superposition of the scattered fields and free fields solved by dynamic stiffness method. With aid of the dynamic 2.5D moving Green's functions (Ba et al. 2017b), this method has the merit of revealing the complex 3D wave-field characteristics, and the calculation domain being restricted to the cross section of topographies without the need of complex 3D discretization. The present formulations are validated by comparison with the published results, and by taking a semi-circular canyon as well as a semi-circular hill topographies as examples, selected numerical simulations are performed in both the frequency and time domains. Results show that the dynamic response for the TI medium differs remarkably from those for the isotropic case, simultaneously depending on incident angle and frequency of excitations. The amplification effects of the hill become prominent with the increase of Eh/Ev, with the displacement amplification more remarkable inside the hill region compared to that of the exterior region.

Wave Reflection and Refraction at the Interface of Triclinic and Liquid Medium

A Mathematical model has been considered to study the reflection and refraction phenomenon of plane wave at the interface of an isotropic liquid medium and a triclinic (anisotropic) half-space. The incident plane qP wave generates three types of reflected waves namely quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH) waves in the triclinic medium and one refracted P wave in the isotropic liquid medium. Expression of phase velocities of all the three quasi waves have been calculated. It has been considered that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation in anisotropic medium. Some specific relations have been established between directions of motion and propagation. The expressions for reflection coefficients of qP, qSV, qSH and refracted P waves with respect to incident qP wave are obtained. Numerical computation and graphical representations have been performed for the reflection coefficient of reflected qP, reflected qSV, reflected qSH and refraction coefficient of refracted P wave with incident qP wave.

Effect of corrugation on incident qP / qSV-waves between two dissimilar nematic elastomers

The problem of the reflection and transmission of elastic waves at a corrugated interface between two dissimilar nematic elastomer half-spaces has been investigated separately for the incident qP and qSV-waves. The expressions of the phase velocities corresponding to qP and qSV-waves are obtained. It is observed that these phase velocities depend on the angle of propagation of the elastic waves. The expression of the amplitude ratios corresponding to the reflected and transmitted waves for the incident qP and qSV-waves is derived by using appropriate boundary conditions. These ratios corresponding to the irregular waves are found to be functions of elastic constants, angle of incidence, coupling constants, characteristic time of rubber relaxation, director rotation times, frequency and corrugation parameter. The amplitude ratios are computed numerically for a particular model at different values of corrugation parameter. The energy distribution of various reflected and transmitted waves is also obtained analytically and numerically.

Wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces

The paper analyses the wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces. The two piezoelectric half-spaces (left and right) are both AlN materials, the middle piezoelectric semiconductor slab is ZnO material and is assumed to be transversely isotropic. The semiconductor effect is emphasized by considering the coupling mechanical displacement, electric potential and the carrier in the slab. The state transition differential equation is derived based on the reduction of order of the governing equations and the transfer matrix of state is obtained by solving the state transition equation. The present method can deal with not only the homogeneous slab but also the heterogeneous slab. Two cases (incident QP wave and incident QSV wave) are considered, and the energy reflection and transmission coefficients varying with the incident angle are calculated. The results show that the steady carrier density and the exterior biasing electric field have obvious influences on the reflection and transmission coefficients. This investigation provides a new thought for the adjustment and controlling of elastic wave propagation in the laminated structures.

Reflection/refraction of qP/qSV wave in layered self-reinforced media

The work in this paper is concentrated on reflection/refraction phenomena of plane qP/qSV wave through a self-reinforced elastic layer sandwiched between two monoclinic half-spaces. A theoretical approach is given to compute the analytical expressions for reflection and transmission coefficients showing their dependence on relevant parameters. Numerical simulation are performed for a fiber – epoxy resin composites self-reinforced layer sandwiched between Lithium niobate like monoclinic upper and lower strata. Using numerical simulation, dependence of reflection/transmission angles, reflected/transmitted velocities and reflection/transmission coefficient are studies against variation in angle of incidence, normalized wave number and the self-reinforcement parameters for both incident qP and qSV waves. It is found that the resultant deflection angles, velocity and reflection/transmission coefficients are significantly dependent upon elastic coefficients of the media as well as on the self-reinforced parameters. Findings of this paper may help seismologists and geophysicists to enhance knowledge about the rock structures and their elastic properties.

Influences of mechanically and dielectrically imperfect interfaces on the reflection and transmission waves between two piezoelectric half spaces

The influences of mechanically and dielectrically imperfect interfaces on the reflection and transmission waves between two piezoelectric half spaces are studied in this paper. First, the secular equations in the traverse isotropic piezoelectric half space are derived from the general dynamic equation. Then, six kinds of imperfect interfaces are considered. These imperfect interfaces include: the mechanically compliant, dielectrically weakly conducting imperfect interface; the mechanically compliant, dielectrically highly conducting imperfect interface; the grounded metallized interface and the low-dielectric interface and their mechanical counterpart, namely, the fixed interface and the slippery interface. These imperfect interface conditions are required to be satisfied by four sets of waves, namely, the quasi-longitudinal wave (QP), the quasi-transverse wave (QSV), the shear horizontal wave (SH) which is decoupled to other waves and the electric-acoustic wave (EA). The algebraic equations resulting from the imperfect interface conditions are solved to obtain the amplitude ratio of various waves and furthermore the reflection and transmission coefficients in terms of the energy flux ratio. The numerical results are obtained for the incident QP wave, the incident QSV wave and the incident SH wave and are validated by the energy conservation principle. The effects of these imperfect interfaces are discussed based on the numerical results. The present study provides useful information for the detection of imperfect interface.

Calculation of reflection and transmission coefficients for qP waves incident on a planar interface between isotropic and triclinic media

In the paper by Chattopadhyay and Rajneesh (2006, “Reflection and refraction of waves at the interface of an isotropic medium over a highly anisotropic medium’, Acta Geophysica, vol. 54, no. 3, pp. 239–249), the authors proposed a process to calculate R/T (reflection and transmission) coefficients at the interface between isotropic and triclinic half-spaces, with incident qP waves in triclinic media. Unfortunately, besides several misprints, the authors made a fatal assumption that there is no transmitted SH wave generated in isotropic media, which led the successive analytical derivations and numerical calculations thoroughly wrong. In this paper, the errors are analyzed at length and corrections are given. Then an alternative approach to solve the problem is proposed and numerical results are shown and discussed.

Wave Reflection in Triclinic Crystalline Medium

In this paper, the reflection of a plane wave at a traction free boundary of a half -space composed of triclinic crystalline material is considered. It is shown that an incident plane wave generates three plane waves, namely quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH) waves governed by the propagation condition involving the acoustic tensor. A simple procedure is presented for the calculation of all the three phase velocities of these waves. It is demonstrated that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation. A procedure is established for the calculation of the amplitude vector in terms of the phase velocity, the propagation vector, and the stiffness coefficients of the medium. Closed form solutions are obtained for the reflection coefficients of qP, qSV and qSH waves. Using the parameters of Vosges sandstone exhibiting triclinic symmetry, the graphical representations of the reflection coefficients due to an incident qP wave are given. It is observed that, in triclinic medium, the reflection coefficients are significantly different from those in an isotropic medium.

Wave reflection and refraction in triclinic crystalline media

In this paper, the reflection and refraction of a plane wave at an interface between two half-spaces composed of triclinic crystalline material is considered. It is shown that due to incidence of plane wave three types of waves, namely quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH), will be generated governed by the propagation condition involving the acoustic tensor. A simple procedure has been presented for the calculation of all the three phase velocities of the quasi waves. It has been established that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation. Relations are established between directions of motion and propagation, respectively. The expressions for reflection and refraction coefficients of qP, qSV and qSH waves are obtained. Numerical results of reflection and refraction coefficients are presented for different types of anisotropic media and for different types of incident waves. Graphical representations have been made for incident qP waves, and for incident qSV and qSH waves numerical data are presented in tables.

Reflection of quasi-P and quasi-SV waves at the free and rigid boundaries of a fibre-reinforced medium

The propagation of plane waves in fibre-reinforced media is discussed. The expressions of phase velocities of quasi-P (qP) and quasi-SV (qSV) waves propagating in plane symmetry are obtained in terms of propagation vectors. We have established a relation from which the displacement vector can be obtained in terms of the propagation vector. Expressions for the reflection coefficients of qP and qSV waves are obtained. Numerical results of reflection coefficients are obtained and presented graphically. The partition of energy between qP and qSV waves reflected on free and rigid boundaries due to incident qP and qSV waves are also obtained and presented graphically.