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EN
The present study aims to investigate Rayleigh wave propagation in an isotropic sandy layer overlying an isotropic sandy semi-infinite medium, with interface considered to be imperfect (slide contact and dislocation like model). Expressions for displacement components are obtained using the variable separation method. The dispersion frequency equation for the Rayleigh wave propagating in sandy media is derived using suitable boundary conditions. Particular cases, such as when the interface is in smooth contact and when sandy media are replaced by elastic media, are also discussed. Using MATLAB software, the effects of the imperfectness parameter (slide contact and dislocation like model) and sandy parameter on the Rayleigh waves’ phase velocity are investigated and compared with the already obtained results of the dislocation like model. The present study may find useful applications in geophysics, civil engineering and soil mechanics.
EN
This paper is concerned with the study of propagation of Rayleigh waves in a homogeneous isotropic piezo-electric microstretch-thermoelastic solid half-space. The medium is subjected to stress-free, isothermal boundary. After developing a mathematical model, the dispersion curve in the form of polynomial equation is obtained. Phase velocity and attenuation coefficient of the Rayleigh wave are computed numerically. The numerically simulated results are depicted graphically. Some special cases have also been derived from the present investigation.
EN
The governing equations for a homogeneous and isotropic thermoelastic medium are formulated in the context of coupled thermoelasticity, Lord and Shulman theory of generalized thermoelasticity with one relaxation time, Green and Lindsay theory of generalized thermoelasticity with two relaxation times, Green and Nagdhi theory of thermoelasticity without energy dissipation and Chandrasekharaiah and Tzou theory of thermoelasticity. These governing equations are solved to obtain general surface wave solutions. The particular solutions in a halfspace are obtained with the help of appropriate radiation conditions. The two types of boundaries at athe surface of a half-space are considered namely, the stress free thermally insulated boundary and stress free isothermal boundary. The particular solutions obtained in a half-space satisfy the relevant boundary conditions at the free surface of the half-space and a frequency equation for the Rayleigh wave speed is obtained for both thermally insulated and isothermal cases. The non-dimensional Rayleigh wave speed is computed for aluminium metal to observe the effects of frequency, thermal relaxation time and different theories of thermoelasticity.
4
Content available remote Propagation of Rayleigh wave in two-temperature dual-phase-lag thermoelasticity
EN
The governing equations of transversely isotropic dual-phase-lag two-temperature thermoelasticity are solved for the surface wave solutions. The particular solutions in the half-space satisfy the boundary conditions at a thermally insulated /isothermal stress-free surface of a half-space to obtain the frequency equation of the Rayleigh wave for the cases of coupled thermoelasticity, Lord and Shulman thermoelasticity and dual-phase-lag thermoelasticity. Some particular and special cases are obtained. The numerical values of the non-dimensional speed of the Rayleigh wave are computed and shown graphically against frequency, non-dimensional elastic constant and two-temperature parameter. The effects of frequency, two-temperature and dual-phase-lag are observed on the nondimensional speed of Rayleigh wave.
PL
W artykule omówiony zostały badania symulacyjne rozchodzenia się fali drganiowej od wibroizolowanych i nie wibroizolowanych torowisk tramwajowych na przykładzie aglomeracji śląskiej. Opracowano model numeryczny podłoża i przeprowadzono symulację drgań w przypadku drgań torowiska wibroizolowanego oraz torowiska posadowionego na podłożu betonowym. Jako wejście do modelu numerycznego wykorzystano pomiary drgań wykonanych wcześniej. Przeprowadzono symulację i oszacowano wpływ oddziaływań dynamicznych na konstrukcję budynku znajdującego się w pobliżu torowisk i w oparciu o skale SWD oceniono stan zagrożenia konstrukcji. Symulacja potwierdziła że fala drganiowa w gruncie ma charakter fali Rayleigha.
EN
The article discusses simulation of vibration wave propagation in the ground for tram tracks viroisolated and nonvibroisolated on the example of the Silesian agglomeration. The numerical model of the ground was developed and the vibration simulation was performed in the case of vibration of the vibration rail track and the track laid on the concrete substrate. As a input to the numerical model, results of measurements of vibrations made earlier were used. The simulations were carried out and the impact of dynamic loads on the construction of a building near the track and on the basis of SWD scales was assessed. Simulation confirmed that the vibration wave in the ground is a Rayleigh wave type.
EN
The Multichannel Analysis of Surface Waves (MASW) is an increasingly used technique for recognition of a shallow geological structure and estimation of geotechnical parameters, e.g., S-wave velocity, layer density, layer thickness, shear modulus, estimated P-wave velocity, and estimated Poisson ratio. MASW surveys were carried out in two limestone quarries in the southern part of Poland. The experimental areas are characterised by a simple geological structure: consolidated Triassic limestone. Measurement profiles were arranged as a shapely six-pointed star. For each survey line, 12 geophones with 2-meter (Deposit 1) and 3-meter (Deposit 2) spacing were applied. The research allowed to compare P- and S-wave velocity changes with the main crack systems in the studied rock masses.
7
Content available Nonlinear surface elastic waves in materials
EN
This paper is devoted to analysis of the surface nonlinear elastic harmonic waves of four types (Rayleigh and Stoneley harmonic waves within the framework of plane strain state; Love and Mozhaev harmonic wave within the framework of anti-plane strain state). The nonlinear model is based on introducing the Murnaghan elastic potential, which includes both geometrical and physical nonlinearities. Each type of surface waves is discussed in four steps: statement of the problem, nonlinear wave equations, approximate solution (first two approximations), so-me conclusions. A nonlinear analysis of waves required many novelties: new variants of the Murnaghan potential, new nonlinear wave equations and new nonlinear boundary conditions. The nonlinear wave equations were solved by the method of successive approximations. A new approach to analyze the boundary conditions is offered. Some new nonlinear wave effects are observed theoretically: a wave picture is reached by the 2nd harmonic and becomes changing in time of propagation, the wave numbers become depending on the initial amplitude.
PL
Artykuł w sposób przeglądowy przedstawia szerokie możliwości zastosowania interferometrii sejsmicznej. Metoda jest stosunkowo nowa, mając na uwadze pierwsze eksperymenty wykonane w 2001 roku, i aktualnie znajduje się w fazie dynamicznego rozwoju. W pracy omówiono jej zastosowanie w wielu zagadnieniach związanych z odwzorowaniem budowy wnętrza Ziemi oraz warstw przypowierzchniowych, a także zagadnień geoinżynierskich z np. monitorowania czynnych osuwisk. Przedstawione przykłady badań zostały opublikowane w uznanych czasopismach naukowych.
EN
The aim of this paper is to review the wide range of seismic interferometry applications. Despite the fact that only 10 years have passed since the first application was implemented in seismology, seismic interferometry is currently used in many issues beginning with analysis of the Earth´s deep interior and ending with the time-laps velocity changes at active landslides. The presented research results were published in leading scientific journals.
EN
The present investigation deals with the propagation of waves in a micropolar transversely isotropic half space with an overlying inviscid fluid layer. Effects of fluid loading and anisotropy on the phase velocity, attenuation coefficient, specific loss and relative frequency shift. Finally, a numerical solution was carried out for aluminium epoxy material and the computer simulated results for the phase velocity, attenuation coefficient, specific loss and relative frequency shift are presented graphically. A particular case for the propagation of Rayleigh waves in a micropolar transversely isotropic half-space is deduced and dispersion curves are plotted for the same as functions of the wave number. An amplitude of displacements and microrotation together with the path of surface particles are also calculated for the propagation of Rayleigh waves in the latter case.
EN
In the present paper, case wise studies have been made to investigate the existence of Rayleigh surface wave in an earth's crustal layer. In the first case, the layer has been kept sandwiched between a rigid boundary plane and a sandy half space, while in the second case the sandy half space has been replaced by an elastic half space with void pores. The dispersion relation has been deduced in both the cases subjected to certain boundary conditions. The phase velocity has been calculated numerically and the effect of sandy parameter, rigid boundary, wave number, inhomogeneity parameter and void parameter on it has been illustrated and displayed by means of graphs. It has been found that the phase velocity of Rayleigh wave is greater when the half space is porous and elastic instead of dry sandy. GUI (graphical user interface) has been developed using MATLAB and a screenshot has been presented in the paper.
EN
The aim of the present paper is to investigate surface waves in an anisotropic, elastic solid medium under the influence of gravity. First, a theory of generalised surface waves was developed and then it was employed to investigate particular cases of waves, viz., Stoneley and Rayleigh, Love type. The wave velocity equations were obtained for different cases and they are in well agreement with the corresponding classical result, when the effect of gravity, viscosity as well as parameters for fibre-reinforcement of the material medium are ignored.
EN
Paper presents results of degradation modelling of historical construction materials based on Rayleigh surface wave velocity (CR) measurement for two marbles widely used as the structural and decorative material in historical constructions. Environmental loading is modelled by freezing and thawing cycles performed in laboratory. Rayleigh wave measurement method does not need any coupling medium between the stone and ultrasonic probe and is 100% non-destructive. It is shown that exponential law can be used to model the proces of degradation of elastic properties of the tested materials.
PL
Praca przedstawia wyniki modelowania degradacji historycznych materiałów konstrukcyjnych na podstawie pomiarów prędkości fali Rayleigha dla dwóch marmurów szeroko stosowanych w zabytkowych budowlach jako materiał konstrukcyjny i dekoracyjny. Obciążenia środowiskowe modelowane są cyklami zamrażania i rozmrażania przeprowadzonymi w laboratorium. Metoda pomiaru fali Rayleigha nie wymaga żadnego ośrodka sprzęgającego pomiędzy materiałem a sondą ultradźwiękową i jest w 100% nieniszcząca. Wykazano, że proces degradacji właściwości sprężystych badanych materiałów dobrze modeluje prawo wykładnicze.
13
Content available remote Propagation of waves in generalized thermoelastic continua with two temperature
EN
The present investigation is concerned with the following two problems. (i) Reflection and transmission of thermoelastic waves between two thermoelastic/ thermoelastic solids with two temperatures at an imperfect interface. The amplitude ratios of different reflected and transmitted waves are obtained and deduced for normal force stiffness, transverse force stiffness, thermal contact conductance and perfect bonding. The variations of amplitude ratios with angle of incidence are shown graphically for the longitudinal wave (P-wave), thermal wave (T-wave) and SV-wave. (ii) Propagation of Rayleigh waves in a thermoelastic half-space with two temperature at the free surface. The phase velocity and attenuation coefficient are obtained and presented graphically to depict the effect of two temperatures. Some special cases of interest are deduced from the present investigation.
14
Content available remote Generalized Rayleigh waves in thermoelastic solids under viscous fluid loading
EN
The paper is aimed to study the propagation of Rayleigh surface waves in a homogeneous isotropic, thermally condueting, and elastic solid halfspace underlying a viscous liquid semi space in the context of generalized theories of thermoelasticity. The investigation is based on modelling the viscous liquid as a hypothetical solid in addition to conduction-convection condition of heat transfer at the interface. After developing the mathematical model, boundary conditions and formal solutions, the secular equations for a thermoelastic solid in closed form and isolated mathematical conditions for generalized Rayleigh waves (Stoneley waves), in complete forms are derived. The amplitude ratios of solid and liquid displacements and temperature change on the surface (interface) are obtained analytically. The surface particle motion has also been discussed and found to be elliptical. The semi-major and semi-minor axes, eccentricity and inclination of major axes with the wave normal are computed analytically and analyzed numerically. The results have been deduced and compared with the relevant publications available in the literature at the appropriate stages of the work. Finally, the numerical solution is carried out for an aluminum-epoxy composite material solid (half space) underlying water, in the case of both light and heavy semi spaces. The dispersion curves, attenuation coefficient profiles and amplitude ratios of surface displacements, temperature change in the solid half space for generalized Rayleigh waves are presented and illustrated graphically in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement. The present analysis is useful in electronics and navigation applications.
15
EN
The propagation of free vibrations in a homogeneous isotropic micropolar viscoelastic plate subjected to stress free conditions is investigated. The secular equations for symmetric and skew symmetric wave mode propagation are derived. The regions of secular equations are obtained and special cases such as Lame modes, thin plate results and short wavelength waves are also discussed. At short wavelength limit, the secular equations for symmetric and skew symmetric waves in a stress free plate reduce to the Rayleigh surface wave frequency equation. The amplitudes of normal force stress, tangential force stress and tangential couple stress are obtained and depicted graphically. Finally, numerical solution is carried out for magnesium crystal composite material plate.
16
Content available remote Propagatlon of Rayleigh-Lamb waves in thermomicrostretch elastic plates
EN
The propagation of waves in a thermo-microstretch elastic plate subjected to stress free isothermal and thermally insulated conditions is investigated in the context of the conventional coupled thermoelasticity (CT), Lord-Shulman (LS), and Green-Lindsay (GL) theories of thermoelasticity. The secular equations for the thermomicrostretch elastic plate in a closed form and isolated mathematical conditions for the symmetric and skewsymmetric wave mode propagation in completely separate terms are derived. The secular equations for the thermo-microstretch elastic plate, coupled thermoelastic, micropolar elastic, thermoelastic and elastic plates have been deduced as particular cases from the secular equations derived. At short wave length limits, the secular equations for the symmetric and skew symmetric waves in stresses free, thermally insulated and isothermal, thermo-microstretch elastic plate reduce to the Rayleigh surface wave's frequency equation. Finally, in order to illustrate the analytical development, the numerical solution is carried out for aluminum-epoxy composite material. The symmetric and skew symmetric wave modes are computed numerically and presented graphically. The theory and numerical computations are found to be in close agreement.
EN
The thermohydrodynamic behavior of the lubricant flow in a Rayleigh step is described by a mathematical model that uses the bidimensional Navier-Stokes and energy equations written in terms of the primary variables u, v, p and T. The non-Newtonian behavior of the lubricant is described by a power law model. The lubricant is assumed to be incompressible and the process is steady-state and laminar. The equations are solved simultaneously using the incremental load method associated with the Newton-Raphson method and the finite element formulation. The effects of a Rayleigh step aspect ratio on the velocities, pressure and temperature patterns for different power law index are investigated.
18
Content available remote Hall effects on MHD plasma Couette flow in a rotating environment
EN
The Magnetohydrodynamic (MHD) plasma Couette flow in a rotating frame of reference subject to the Hall current is studied. This problem is confined to a startup process, which deals with an impulsive start of the moving plate as well as an accelerated start of the moving plate. The solution is obtained by employing the Laplace inversion method. An asymptotic behavior of the solution is analysed for small as well as large time T to gain the physical insight into the flow pattern. As a consequence of the physical situation of interest the fully ionized neutral plasma interacts with the frictional layer when it starts in motion. The dimensionless velocity profiles are depicted graphically and the shear stresses are presented in tables.
19
Content available remote Formulas for the Rayleigh wave speed in orthotropic elastic solids
EN
Formulas for the speed of Rayleigh waves in orthotropic compressible elastic materials are obtained in explicit form by using the theory of cubic equations. Different formulas are obtained by using different forms of the (cubic) secular equation. Each formula is expressed as a continuous function of three dimensionless material parameters, which are the ratios of certain elastic constants. It is interesting to note that one of the formulas includes as a special case the formula obtained recently by Malischewsky for isotropic materials.
EN
A harmonic in time, plane longitudinal wave is incident on a half-space containing a vertical edge crack. Both the incident field as well as the scattered field have been decomposed into symmetric and antisymmetric fields with respect to the plane of the crack, so that the problem is reduced to the boundary value problem for a 90° wedge. In both the symmetric and antisymmetric problem, incident body waves are at first diffracted by the edge of the crack. For a high frequency solution, the diffracted body wave rapidly decreasing after a few wave-lengths, the significant part of the diffracted wave is the Rayleigh wave which is reflected back from the corner of the wedge giving rise to a Rayleigh wave diffracted by the crack tip. This process of reflection of surface wave from the corner of the wedge and subsequent diffraction by the crack tip continues. Considering the contribution from the incident body waves and all the reflected Rayleigh waves, the stress intensity factors have been determined and their dependence on the frequency and on the angle of incidence has been depicted by means of graphs.
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