• Title/Summary/Keyword: Wave equation

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Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface

  • Kim, No-Hyu;Yang, Seung-Yong
    • 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.

Evaluation of Average Shear-wave Velocity Estimation Methods of Multi-layered Strata Considering Site Period (지반주기를 고려한 다층지반의 평균전단파속도 추정 방법 평가)

  • Kim, Dong-Kwan
    • Journal of the Earthquake Engineering Society of Korea
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    • v.23 no.3
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    • pp.191-199
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    • 2019
  • To calculate proper seismic design load and seismic design category, the exact site class for construction site is required. At present, the average shear-wave velocity for multi-layer soil deposits is calculated by the sum of shear-wave velocities without considering of vertical relationship of the strata. In this study, the transfer function for the multi-layered soil deposits was reviewed on the basis of the wave propagation theory. Also, the transfer function was accurately verified by the finite element model and the eigenvalue analysis. Three methods for site period estimation were evaluated. The sum of shear-wave velocities underestimated the average shear-wave velocities of 526 strata with large deviations. The equation of Mexican code overestimated the average shear-wave velocities. The equation of Japanese code well estimated the average shear-wave velocities with small deviation.

Internal Wave-Maker using Momentum Source Term of RANS Equation Model (RANS 방정식의 운동량 원천항을 이용한 내부조파)

  • Choi, Jun-Woo;Ko, Kwang-Oh;Yoon, Sung-Bum
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.21 no.2
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    • pp.182-190
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    • 2009
  • For RANS equation model using VOF scheme Lin and Liu (1999) developed internal wave-maker method to generate target wave trains by using designed mass source functions of the continuity equation. By using this method studies on various numerical wave experiments has been achieved without the problem caused by wave reflection due to an external wave-maker. In this study, the wave-maker method to generate target wave trains by using a momentum source function was proposed. The computational results obtained by applying the mass and momentum source functions into FLUENT were compared with each other. To see its applicability, the hydraulic experiment of Luth et al. (1994) were numerically simulated and their measurements are compared with the computations, and the vertical variations of computed results were shown and investigated.

Characteristics of Wave Trasnformation in Gamcheon Harbor (감천항내의 파랑변형 특성)

  • 김재중;김기철;이정만
    • Journal of Korean Port Research
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    • v.13 no.2
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    • pp.399-408
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    • 1999
  • Copeland’s(1985) hyperbolic mild-slope equation including diffraction refraction and reflection in the wave field is used as a governing equation in this study. The result of Maruyama & Kajima(1985) is used to calculate wave direction and that of Watanabe & Maruyama(1986) is used as a energy dissipation formula. Numerical solutions are obtained by the Leap-Frog scheme and compared with Watanabe & Maruyama’s (1984) hydraulic experimental results and numerical simulation results for the detached breakwater. This wave model is applied to a detached breakwater and compared with Watanabe and Maruyama’s (1984) hydraulic model results to check the characteristics of reflected wave field around a detached breakwater. The distribution of wave height and we phase in front of a detached breakwater is more accurate than the Watanabe and Maruyama’s numerical results. The results from our wave model show good agreements with the others and also show nonlinear effects around the detached breakwater. This model is applied to the Gamcheon harbor of pusan. the field observations were carried out at Pusan harbor wave station in 1986-1995 and the results were accepted as a design wave condition in this study. The wave height and wave period was measured by Dong-A university at one station in the Gamcheon harbor in 1996-1997 and used as a calibration criterion. The measured data were used as input data for the numerical simulation and also compared with simulated results. The numerical simulation shows a fairly good results which considering the effect of topographic characteristics and effect of narrow entrance due to two separated breakwaters in Gamcheon harbor. The wave distribution characteristics inside Gamcheon harbor is quite different with the offshore wave direction and wave period.

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Determination of Wave Equation Soil Constants by Standard Penetration Test (표준관입시험을 통한 파동방정식 지반정수 산정법)

  • 김범상;김기영;조성민
    • Journal of the Korean Geotechnical Society
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    • v.18 no.4
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    • pp.45-53
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    • 2002
  • There are some previous studies on the determination wave equation soil constants by SPT. However, methods suggested in previous researches had such analytical defects as the non-uniqueness of solutions, long-time consuming in computation, and lacking of accuracy due to the limit of available point values in time domain. In this paper, a modified procedure is proposed to improve the accuracy of determination of wave equation soil constants. It is based upon the least-error approach which minimizes the sum of errors between the measured and the recalculated wave values in total time domain. Finally, its applicability was verified by analyzing measured data presented on the released references.

On Propagation of Love waves in dry sandy medium sandwiched between fiber-reinforced layer and prestressed porous half-space

  • Gupta, Shishir;Ahmed, Mostaid
    • Earthquakes and Structures
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    • v.12 no.6
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    • pp.619-628
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    • 2017
  • The intent of this paper is to investigate the propagation of Love waves in a dry sandy medium sandwiched between fiber-reinforced layer and prestressed porous half-space. Separate displacement components have been deduced in order to characterize the dynamics of individual materials. Using suitable boundary conditions, the frequency equation has been derived by means of separation of variables which reveals the significant role of reinforcement parameters, sandiness, thickness of layers, porosity and prestress on the wave propagation. The phase velocity of the Love wave has been discussed in accordance with its typical cases. In both cases when fiber-reinforced and dry sandy media are absent, the derived equation of Love type wave coincides with the classical Love wave equation. Numerical computations have been performed in order to graphically illustrate the dependencies of different parameters on phase velocity of Love waves. It is observed that the phase velocity decreases with the increase of parameters pertaining to reinforcement and prestress. The results have certain potential applications in earthquake seismology and civil engineering.

NUMERICAL SIMULATIONS OF FULLY NONLINEAR WAVE MOTIONS IN A DIGITAL WAVE TANK (디지털 파랑 수조 내에서의 비선형 파랑 운동의 수치시뮬레이션)

  • Park, J.C.;Kim, K.S.
    • Journal of computational fluids engineering
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    • v.11 no.4 s.35
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    • pp.90-100
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    • 2006
  • A digital wave tank (DWT) simulation technique has been developed by authors to investigate the interactions of fully nonlinear waves with 3D marine structures. A finite-difference/volume method and a modified marker-and-cell (MAC) algorithm have been used, which are based on the Navier-Stokes (NS) and continuity equations. The fully nonlinear kinematic free-surface condition is implemented by the marker-density function (MDF) technique or the Level-Set (LS) technique developed for one or two fluid layers. In this paper, some applications for various engineering problems with free-surface are introduced and discussed. It includes numerical simulation of marine environments by simulation equipments, fully nonlinear wave motions around offshore structures, nonlinear ship waves, ship motions in waves and marine flow simulation with free-surface. From the presented simulations, it seems that the developed DWT simulation technique can handle various engineering problems with free-surface and reliably predict hydrodynamic features due to the fully-nonlinear wave motions interacting with such marine structures.

Inhomogeneous Helmholtz equation for Water Waves on Variable Depth (비균질 Helmholtz 방정식을 이용한 변동 수심에서의 파랑변형)

  • Kim, Hyo-Seob;Jang, Chang-Hwan
    • Journal of the Korean Society for Marine Environment & Energy
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    • v.13 no.3
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    • pp.174-180
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    • 2010
  • The inhomogeneous Helmholtz equation is introduced for variable water depth and potential function and separation of variables are introduced for the derivation. Only harmonic wave motions are considered. The governing equation composed of the potential function for irrotational flow is directly applied to the still water level, and the inhomogeneous Helmholtz equation for variable water depth is obtained. By introducing the wave amplitude and wave phase gradient the governing equation with complex potential function is transformed into two equations of real variables. The transformed equations are the first and second-order ordinary differential equations, respectively, and can be solved in a forward marching manner when proper boundary values are supplied, i.e. the wave amplitude, the wave amplitude gradient, and the wave phase gradient at a side boundary. Simple spatially-centered finite difference numerical schemes are adopted to solve the present set of equations. The equation set is applied to two test cases, Booij’ inclined plane slope profile, and Bragg’ wavy bed profile. The present equations set is satisfactorily verified against other theories including the full linear equation, Massel's modified mild-slope equation, and Berkhoff's mild-slope equation etc.

Travel Time Calculation Using Mono-Chromatic Oneway Wave Equation (단일주파수 일방향파동방정식을 이용한 주시계산)

  • Shin, Chang-Soo;Shin, Sung-Ryul;Kim, Won-Sik;Ko, Seung-Won;Yoo, Hai-Soo
    • Geophysics and Geophysical Exploration
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    • v.3 no.4
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    • pp.119-124
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    • 2000
  • A new fast algorithm for travel time calculation using mono-chromatic one-way wave equation was developed based on the delta function and the logarithms of the single frequency wavefield in the frequency domain. We found an empirical relation between grid spacing and frequency by trial and error method such that we can minimize travel time error. In comparison with other methods, travel time contours obtained by solving eikonal equation and the wave front edge of the snapshot by the finite difference modeling solution agree with our algorithm. Compared to the other two methods, this algorithm computes travel time of directly transmitted wave. We demonstrated our algorithm on migration so that we obtained good section showing good agreement with original model. our results show that this new algorithm is a faster travel time calculation method of the directly transmitted wave for imaging the subsurface and the transmission tomography.

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The Characteristic of Wave Propagation in the Irregular Wave-current field (불규칙파.흐름 공존장에서 파랑변동특성)

  • Lee, Chang-Ho;Kim, Heon-Tae;Ryu, Cheong-Ro;Lee, In-Cheol
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2003.05a
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    • pp.128-134
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    • 2003
  • Numerical study on interactions of waves and currents has considerable practical interests in coastal and ocean engineering. And wave-current interactions strongly influence wave characteristics, current profiles, and forces on offshore structures. Presence of currents affects wave properties such as wave height and wave profiles. Furthermore, in case of the irregular waves, it is more complicated problem. The propose of present study, using the one-dimensional wave-current numerical model is based on the extended Boussinesq equation(Madsen, 1991) and an alternative form of wave-current dispersion relation(Mohiuddin, 1999, 2000) including wave action concept, is to simulate wave propagation in a current field including the irregular waves and discuss applicability of the model in a wave-current field.

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