• Steel and Composite Structures
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• v.50 no.2
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• pp.123-133
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• 2024

The paper deals with the propagation of Rayleigh waves in a nonlocal thermoelastic isotropic layer which is lying over a nonlocal thermoelastic isotropic half-space under the purview of Green-Lindsay model and Eringen's nonlocal elasticity in the presence of voids. The normal mode analysis is employed to the considered equations to obtain vector matrix differential equation which is then solved by eigenvalue approach. The frequency equation of Rayleigh waves is derived and different particular cases are also deduced. The effects of voids and nonlocality on different characteristics of Rayleigh waves are presented graphically.

• Smart Structures and Systems
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• v.29 no.2
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• pp.279-286
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• 2022

In this article, a novel propagation formulation of Rayleigh waves in a compressible isotropic half-space with impedance boundary condition is proposed by embedding the normal stress. In a two-dimensional case, it is assumed that a design boundary is free of normal traction and a shear traction depends on linearly a normal component of displacements multiplied by frequencies. Therefore, impedance boundary conditions affect the normal stress, where the impedance parameters correspond to dimensions of stresses over velocity. On the other hand, vanished impedance values are traction-free boundary conditions. The main purpose of this article is to present theoretically the existence and uniqueness of a Rayleigh wave formulation relying on secular equation's mathematical analyses. Its velocity varies along with the impedance parameters. Moreover, numerical experiments with different values for the velocity of Rayleigh waves are carried out. The present Rayleigh waves study is a fundamental step in analyzing the cause and effect of physical states such as building or structure damages resulting from natural dynamics. The results of the study generate a basic design formulation theory to test the effects of Rayleigh waves affecting structures when an earthquake occurs. The presence and uniqueness of the proposed formulation is verified by mutual comparisons of several numerical examples.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2006.11a
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• pp.367-372
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• 2006

If the sea is narrowband, the Rayleigh distribution introduced by Longuet-Higgins can be used for the individual wave height distribution. However the Rayleigh distribution over-predicts the probability of high waves. Longuet-Higgins introduced alternative form of the Rayleigh distribution with an empirical constant. The wave height distribution can be fitted well by one parameter Rayleigh distribution with a proper choice of the empirical constant. The empirical constant is the ratio of the significant wave height based the time domain analysis and the spectral analysis. Here we examine wave data which contain extreme waves. Once again we confirmed that extreme wave height distribution can be modelled well by a modified Rayleigh distribution.

• Journal of the Korean Society for Marine Environment & Energy
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• v.13 no.2
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• pp.112-120
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• 2010

In this paper time series wave data measured continuously for 24 hours during a storm in Yura Sea Area are used to investigate statistical characteristics of nonlinear waves. The exceedance probability of wave height is compared using the Rayleigh distribution and the Edgeworth-Rayleigh (ER) distribution. Wave data which show stationary state for 10 hours contain 4600 waves approximately. The Gram-Chalier distribution fits the probability of wave elevation better than the Gaussian distribution. The Rayleigh ($H_{rms}$) distribution follows the exceedance probability of wave height in general and predicts the probability of freak waves well. The ER distribution overpredicts the exceedance probability of wave heights and the occurrence of freak waves. If wave data measured for 30 minute period which contains 250 waves are used, the ER distribution can predict the occurrence probability of freak waves well. But it overpredicts the probability of overall wave height If no freak wave occurs, the Rayleigh ($H_{rms}$) distribution agrees well with wave height distribution for the most of wave height ranges. The wave height distribution of freak waves of which height are less than 10 m shows similar tendency compared with freak waves greater than 10 m. The value of $H_{max}/H_{1/3}$ is related to the kurtosis of wave elevation. It seems that there exists threshold value of the kurtosis for the occurrence of freak waves.

• 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.

• Journal of the Korean Society for Nondestructive Testing
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• v.27 no.6
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• pp.582-590
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• 2007

Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness.

• 한국지구물리탐사학회:학술대회논문집
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• 2005.05a
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• pp.233-236
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• 2005

Polarization filtering based on the multicomponent complex trace analysis method is performed to reject Rayleigh waves and to enhance S waves. To test the polarization filter, synthetic seismic data were constructed for a simple two-layer model based on the finite difference method. Rayleigh waves with elliptic motion are eliminated effectively and P and S waves with linear motions are well separated each other.

• Journal of the Korean Geophysical Society
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• v.8 no.1
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• pp.35-38
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• 2005

Polarization filtering based on the multicomponent complex trace analysis method is performed to reject Rayleigh waves and to enhance S waves. To test the polarization filter, synthetic seismic data were constructed for a simple two-layer model based on the finite difference method. Rayleigh waves with elliptic motion are eliminated effectively and P and S waves with linear motions are well separated each other.

• Geomechanics and Engineering
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• v.10 no.2
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• pp.137-154
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• 2016

The purpose of this paper is to study the propagation of Rayleigh waves in an anisotropic heterogeneous crustal layer over a gravitational semi-infinite sandy substratum. It is assumed that the heterogeneity in the crustal layer arises due to exponential variation in elastic coefficients and density whereas the semi-infinite sandy substratum has homogeneous sandiness parameters. The coupled effects of heterogeneity, anisotropy, sandiness parameters and gravity on Rayleigh waves are discussed analytically as well as numerically. The dispersion relation is obtained in determinant form. The proposed model is solved to obtain the different dispersion relations for the Rayleigh wave in the elastic medium of different properties. The results presented in this study may be attractive and useful for mathematicians, seismologists and geologists.

• Advances in materials Research
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• v.12 no.3
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• pp.211-226
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• 2023

The present work is considered to study the two-dimensional problem in an orthotropic magneto-thermoelastic media and examined the effect of thermal phase-lags and GN-theories on Rayleigh waves in the light of fractional order theory with combined effect of rotation and hall current. The boundary conditions are used to derive the secular equations of Rayleigh waves. The wave properties such as phase velocity, attenuation coefficient are computed numerically. The numerical simulated results are presented graphically to show the effect of phase-lags and GN-theories on the Rayleigh wave phase velocity, attenuation coefficient, stress components and temperature change. Some particular cases are also discussed in the present investigation.