• Structural Engineering and Mechanics
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• v.77 no.4
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• pp.473-479
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• 2021

The propagation of plane waves in a linear, homogeneous and isotropic nonlocal generalized thermoelastic solid medium is considered in the framework of Lord and Shulman generalization. The governing field equations are formulated and specialized in a plane. Plane wave solutions of governing equations show that there exists three plane waves, namely, P, thermal and SV waves which propagate with distinct speeds. Reflection of P and SV waves from thermally insulated or isothermal boundary of a half-space is considered. The relevant boundary conditions are applied at stress free boundary and a non-homogeneous system of three equations in reflection coefficients is obtained. For incidence of both P and SV waves, the expressions for energy ratios of reflected P, thermal and SV waves are also obtained. The speeds and energy ratios of reflected waves are computed for relevant physical constants of a thermoelastic material. The speeds of plane waves are plotted against nonlocal parameter and frequency. The energy ratios of reflected waves are also plotted against the angle of incidence of P wave at a thermally insulated stress-free surface. The effect of nonlocal parameter is shown graphically on the speeds and energy ratios of reflected waves.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.1
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• pp.16-28
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• 2007

The results of experimental investigation of coherent structures beneath wind-generated waves in deep water are presented. Vorticity fields of deepwater wind waves were visualized by analyzing the velocity fields obtained by PIV measurements under different wind and fetch conditions. In addition, spatio-temporal evolution of the coherent structures and subsequent changes in vertical profiles of the instantaneous vorticity were qualitatively examined. It was found that a coherent structure is formed right underneath the wave crest and traveled in phase with the surface wave. The direction of rotation of the coherent structure was contrary to the wave orbital motion when wind speed is less than 10 m/s, while was same as the wave orbital motion when wind speed is approximately 13 m/s and wave breaking occurs at the wave crest. In the near-surface region, complex vortex-vortex interactions were observed according to the traveling of the coherent structure. In contrast, coherent structures far below the water surface changed little due to weak influence of orbital motion by the surface waves.

• Geomechanics and Engineering
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• v.15 no.1
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• pp.645-657
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• 2018

The paper aims to analyze the behaviour of torsional type surface waves propagating through fluid saturated inhomogeneous porous media clamped between two inhomogeneous anisotropic media. We considered three types of inhomogeneities in upper anisotropic layer which varies exponentially, quadratically and hyperbolically with depth. The anisotropic half space inhomogeneity varies linearly with depth and intermediate layer is taken as inhomogeneous fluid saturated porous media with sinusoidal variation. Following Biot, the dispersion equation has been derived in a closed form which contains Whittaker's function and its derivative, for approximate result that have been expanded asymptotically up to second term. Possible particular cases have been established which are in perfect agreement with standard results and observe that when one of the upper layer vanishes and other layer is homogeneous isotropic over a homogeneous half space, the velocity of torsional type surface waves coincides with that of classical Love type wave. Comparative study has been made to identify the effects of various dimensionless parameters viz. inhomogeneity parameters, anisotropy parameters, porosity parameter, and initial stress parameters on the torsional wave propagation by means of graphs using MATLAB. The study has its own relevance in connection with the propagation of seismic waves in the earth where fluid saturated poroelastic layer is present.

• Geomechanics and Engineering
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• v.14 no.1
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• pp.19-27
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• 2018

It follows from the basic principles of mechanics of deformable solids relating to the strength, stability and propagation of elastic waves that the Earth's inner core cannot exist in the form of a spherical structure in the assumed thermobaric conditions and calculation values of physico-mechanical parameters. Pressure level reaches a value that is significantly greater than the theoretical limit of medium strength in the model approximations at the surface of the sphere of the inner core. On the other hand, equilibrium state of the sphere is unstable on the geometric forming at much lower loads under the influence of the "dead" surface loads. In case of the action of "follower" loads, the assumed pressure value on the surface of the sphere is comparable with the value of the critical load of "internal" instability. In these cases, due to the instability of the equilibrium state, propagation of homogeneous deformations becomes uneven in the sphere. Moreover, the elastic waves with actual velocity cannot propagate in such conditions in solid medium. Violation of these fundamental conditions of mechanics required in determining the physical and mechanical properties of the medium should be taken into account in the integrated interpretations of seismic and laboratory (experimental) data. In this case, application of the linear theory of elasticity and elastic waves does not ensure the reliability of results on the structure and composition of the Earth's core despite compliance with the required integral conditions on the mass, moment of inertia and natural oscillations of the Earth.

• International Journal of Naval Architecture and Ocean Engineering
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• v.11 no.2
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• pp.819-827
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• 2019

Bragg reflection of water waves by three kinds of surface-piercing fixed structures with rectangular, cosinoidal and triangular shapes is studied. Boundary element method is used to analyze the wave scattering by these structures based on the linear wave theory. Results of reflection and transmission coefficients are validated by comparing with those available in literature. These structures with proper configurations are proved to be effective in attenuating waves by using Bragg reflection, and the triangular structures are found to be the best choices among the structures with same width and same area. Systematic calculations are then carried out for the triangular structures by varying the number, the draft, the width, the gap and the combination of width and gap of the structures to analyze their influences on the characteristics of Bragg reflection. The results are of reference values for design of the structures to attenuate waves based on the Bragg reflection.

• Proceedings of the Korean Geotechical Society Conference
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• 1995.10a
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• pp.15.2-22
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• 1995

Evaluating stiffness of near-surface materials has been one of the critically important tasks in many civil engineering works. It is the main goal of geotechnical characterization. The so-called deflection-response method evaluates the stiffness by measuring stress-strain behavior of the materials caused by static or dynamic load. This method, however, evaluates the overall stiffness and the stiffness variation with depth cannot be obtained. Furthermore, evaluation of a large-area geotechnical site by this method can be time-consuming, expensive, and damaging to many surface points of the site. Wave-propagation method, on the other hand, measures seismic velocities at different depths and stiffness profile (stiffness change with depth) can be obtained from the measured velocity data. The stiffness profile is often expressed by shear-wave (S-wave) velocity change with depth because S-wave velocity is proportional to the shear modulus. that is a direct indicator of stiffiiess. The crosshole and downhole method measures the seismic velocity by placing sources and receivers (geophones) at different depths in a borehole. Requirement of borehole installation makes this method also time-consuming, expensive, and damaging to the sites. Spectral-Analysis-of-Surface-Waves (SASW) method places both source and receivers at the surface, and records horizontally-propagating surface waves. Based upon the theory of surfacewave dispersion, the seismic velocities at different depths are calculated by analyzing the recorded surface-wave data. This method can be nondestructive to the sites. However, because only two receivers are used, the method requires multiple measurements with different field setups and, therefore, the method often becomes time-consuming and labor-intensive. Furthermore. the inclusion of noise wavefields cannot be handled properly, and this may cause the results by this method inaccurate. When multi-channel recording method is employed during the measurement of surface-waves, there are several benefits. First, usually single measurement is enough because multiple number (twelve or more) of receivers are used. Second, noise inclusion can be detected by coherency checking on the multi-channel data and handled properly so that it does not decrease the accuracy of the result. Third, various kinds of multi-channel processing techniques can be applied to f1lter unwanted noise wavefields and also to analyze the surface-wavefields more accurately and efficiently. In this way, the accuracy of the result by the method can be significantly improved. Fourth, the entire system of source, receivers, and recording-processing device can be tied into one unit, and the unit can be pulled by a small vehicle, making the survey speed very fast. In all these senses, multi-channel recording of surface waves is best suited for a routine method for geotechnical characterization in most of civil engineering works.

• Geophysics and Geophysical Exploration
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• v.7 no.1
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• pp.7-13
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• 2004

In this paper, we demonstrate that Common Mid-Point (CMP) cross-correlation gathers of multi-channel and multi-shot surface waves give accurate phase-velocity curves, and enable us to reconstruct two-dimensional (2D) velocity structures with high resolution. Data acquisition for CMP cross-correlation analysis is similar to acquisition for a 2D seismic reflection survey. Data processing seems similar to Common Depth-Point (CDP) analysis of 2D seismic reflection survey data, but differs in that the cross-correlation of the original waveform is calculated before making CMP gathers. Data processing in CMP cross-correlation analysis consists of the following four steps: First, cross-correlations are calculated for every pair of traces in each shot gather. Second, correlation traces having a common mid-point are gathered, and those traces that have equal spacing are stacked in the time domain. The resultant cross-correlation gathers resemble shot gathers and are referred to as CMP cross-correlation gathers. Third, a multi-channel analysis is applied to the CMP cross-correlation gathers for calculating phase velocities of surface waves. Finally, a 2D S-wave velocity profile is reconstructed through non-linear least squares inversion. Analyses of waveform data from numerical modelling and field observations indicate that the new method could greatly improve the accuracy and resolution of subsurface S-velocity structure, compared with conventional surface-wave methods.

• International Journal of Naval Architecture and Ocean Engineering
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• v.2 no.1
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• pp.34-38
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• 2010

Field investigations have been carried out in two 60-day stages on the surf beat low frequency waves in Anzali port, one of the main commercial ports in Iran, located in southwest coast of the Caspian Sea. The characteristics of significant water waves were measured at three metering stations in the sea, one at the entrance of the port and three in the basin. The measured data were inspected to investigate the surf beat negative effects on the tranquility of the port. Using field measurements and complementary numerical modeling, the response of the basin to the infra-gravity long waves was inspected for a range of wave frequencies. It was concluded that the water surface fluctuations in the port is strongly related to the incident wave period. The long waves with periods of about 45s were recognized as the worst cases for water surfaceperturbation in the port. For wave periods higher than the mentioned range, the order of fluctuation was generally low.

• Earthquakes and Structures
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• v.9 no.1
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• pp.111-126
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• 2015

In this study, the coupled effects of magnetic field, stress and thermal field on gravity waves propagating in a liquid layer over a solid surface are discussed. Due to change in temperature, initial hydrostatic stress and magnetic field, the gravity-sound Rayleigh waves can propagate in the liquid-solid interface. Dispersion properties of waves are derived by using classical dynamical theory of thermoelasticity. The phase velocity of gravity waves influenced quite remarkably in the presence of initial stress parameter, magneto-thermoelastic coupling parameter in the half space. Numerical solutions are also discussed for gravity-Rayleigh waves. In the absence of temperature, stress and magnetic field, the obtained results are in agreement with classical results.

• Ocean Systems Engineering
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• v.1 no.4
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• pp.355-372
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• 2011

Based on the fully nonlinear velocity potential theory, the liquid sloshing in a three dimensional tank under random excitation is studied. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing scheme, B-spline curve, is applied to both the longitudinal and transverse directions of the tank to eliminate the possible saw-tooth instabilities. When the tank is undergoing one dimensional regular motion of small amplitude, the calculated results are found to be in very good agreement with linear analytical solution. In the simulation, the normal standing waves, travelling waves and bores are observed. The extensive calculation has been made for the tank undergoing specified random oscillation. The nonlinear effect of random sloshing wave is studied and the effect of peak frequency used for the generation of random oscillation is investigated. It is found that, even as the peak value of spectrum for oscillation becomes smaller, the maximum wave elevation on the side wall becomes bigger when the peak frequency is closer to the natural frequency.