• The Journal of the Acoustical Society of Korea
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• v.20 no.4
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• pp.54-61
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• 2001

Magnetostrictive materials have nonlinear elasto-magnetic properties. However the constitutive equations to describe the nonlinear properties are not available, yet. In this study we develope the equation in magnetostrictive materials by use of piezomagnetic constitutive equation which is quasi-linearized. With the wave equation, we determine the propagation velocity inside the magnetostrictive materials when a plane wave propagates along a given magnetic field. Validity of the calculated velocity is verified through comparison with experimental velocity measurement results for the most representative magnetostrictive materials. Terfenol-D.

• Journal of Ocean Engineering and Technology
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• v.18 no.4 s.59
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• pp.40-45
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• 2004

An efficient numerical model of the modified mild slope equation, based on the robust iterative method is presented. The model developed is verified against other numerical experimental results, related to wave reflection from an arc-shaped bar and wave transformation over a circular shoal. The results show that the modified mild slope equation model is capable of producing accurate results for wave propagation in a region where water depth varies substantially, while the conventional mild slope equation model yeilds large errors, as the mild slope assumption is violated.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.209-212
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• 2002

Since Berkhoff proposed the mild-slope equation in 1972, it has widely been used for calculation of shallow water wave transformation. Recently, it was extended to give an extended mild-slope equation, which includes the bottom slope squared term and bottom curvature term so as to be capable of modeling wave transformation on rapidly varying topography. These equations were derived by integrating the Laplace equation vertically. In the present study, we develop a finite element model to solve the Laplace equation directly while keeping the same computational efficiency as the mild-slope equation. This model assumes the vertical variation of wave potential as a cosine hyperbolic function as done in the derivation of the mild-slope equation, and the Galerkin method is used to discretize . The computational domain was discretized with proper finite elements, while the radiation condition at infinity was treated by introducing the concept of an infinite element. The upper boundary condition can be either free surface or a solid structure. The applicability of the developed model was verified through example analyses of two-dimensional wave reflection and transmission. .

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.2 no.3
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• pp.128-133
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• 1990

An equation is presented to calculate wave height due to shoaling, refraction and bottom friction. The equation in an integral form is evaluated by two different methods： A numerical method and an analytical method based on approximation. Both methods are used to calculate wave height and show very good agreement between their results. As shown in the figure of wave height variation vs. relative water depth, an increase of incident angle leads to a decrease in wave height. For the case of normal incident wave, the present equation can be reduced, under some assumptions, to the existing equation of Bretschneider and Reid (1954).

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.11-27
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• 2015

Nonlinear partial differential equations are more suitable to model many physical phenomena in science and engineering. In this paper, we consider three nonlinear partial differential equations such as Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation which serves as a model for the unidirectional propagation of the shallow water waves over a at bottom. The main objective in this paper is to apply the generalized Riccati equation mapping method for obtaining more exact traveling wave solutions of Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation. More precisely, the obtained solutions are expressed in terms of the hyperbolic, the trigonometric and the rational functional form. Solutions obtained are potentially significant for the explanation of better insight of physical aspects of the considered nonlinear physical models.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.12 no.4
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• pp.181-189
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• 2000

A weakly nonlinear mild-slope equation has been derived directly from the continuity equation with the aid of the Galerkin's method. The equation is combined with the momentum equations defined at the mean water level. A single component model has also been obtained in terms of the surface displacement. The linearized form is completely identical with the time-dependent mild-slope equation proposed by Smith and Sprinks(1975). For the verification purposes of the present nonlinear model, the degenerate forms were compared with Airy(1845)'s non-dispersive nonlinear wave equation, classical Boussinesq equation, andsecond¬order permanent Stokes waves. In this study, the present nonlinear wave equations are discretized by the approximate factorization techniques so that a tridiagonal matrix solver is used for each direction. Through the comparison with physical experiments, nonlinear wave model capacity was examined and the overall agreement was obtained.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.17 no.3
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• pp.202-212
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• 2005

In the design of an of offshore structure located near an underwater shoal, the same amount of attention given to the wave height may have to be put to the wave induced current as well since some of the wave energy translates to the current. In the present study, two numerical models each based on the nonlinear Boussinesq equation and the linear mild slope equation are applied to calculate the wave deformation and secondly induced current around a shoal. The underwater shoal in Vincent and briggs' experiment (1989) is used here, and all non-breaking wave conditions of the experiment with various monochromatic and unidirectional or multidirectional spectral wave incidences are concerned. Both numerical models clearly showed wave induced currents symmetrically farmed along the centerline over the shoal. The calculated wave heights along a preset line also generally showed very nice agreements with the experimental values.

• Journal of Ocean Engineering and Technology
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• v.37 no.6
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• pp.238-246
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• 2023

This paper proposes an effective inertia coefficient (EIC) in the Morison equation for better wave-force calculations. The OC4 semi-submersible floating offshore wind turbine (FOWT) platform was considered to test the feasibility. Large diffraction at large Keulegan-Carpenter (KC) numbers and the interaction between columns can result in errors in estimating the wave force using the Morison equation with a theoretical inertia coefficient, which can be corrected by the EIC as a function of the wave period and direction. The horizontal and vertical wave forces were calculated using the Morison equation and potential theory at each column, wave period, and wave direction. The EICs of each column were then obtained, resulting in a minimal difference between the Morison inertia force and the wave excitation force by the potential theory. The EICs, wave forces, phase angles, and dynamic motions were compared to confirm the feasibility of an EIC concept under regular and random waves.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.49-58
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• 2010

In the present article we consider the diffusive Nicholson's blowflies equation with nonlocal delay incorporated into an integral convolution over all the past time and the whole infinite spatial domain $\mathbb{R}$. When the kernel function takes a special function, we construct a pair of lower and upper solutions of the corresponding travelling wave equation and obtain the existence of travelling fronts according to the existence result of travelling wave front solutions for reaction diffusion systems with nonlocal delays developed by Wang, Li and Ruan (J. Differential Equations, 222(2006), 185-232).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.4
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• pp.381-394
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• 2019

In this paper, we are extending fractional partial differential equations to fuzzy fractional partial differential equation under Riemann-Liouville and Caputo fractional derivatives, namely Variational iteration methods, and this method have applied to the fuzzy fractional wave equation with initial conditions as in fuzzy. It is explained by one and two-dimensional wave equations with suitable fuzzy initial conditions.