• Journal of Korean Society of Coastal and Ocean Engineers
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• v.3 no.1
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• pp.45-53
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• 1991

The nonlinear forward diffraction of a modulated wave train by a thin wedge has been studied analytically. Since the physical variables involved in the problem have vastly different scales, the multiple scale expansion method has been used to obtain an approximate solution. To simplify the problem. the wedge is assumed to be thin and the parabolic approximation is utilized. The wave evolution can be described by a kind of the cubic Schrodinger equation. which consists of the linear time evolution. the lateral dispersion and the nonlinearity. Numerical results indicate that the nonlinearity. which it defined by the ratio of the ratio of the incident wave to the wedge angle. governs the amplitude and the stability of diffracted waves. The instability of dirffracted waves becomes more pronounced as the nonlinearity increases and the modulation ratio decreases. It is also found that the stem waves. initially developed along the wedge. can not sustain for a long time.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.9 no.5
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• pp.139-146
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• 2009

Parametric array for audio applications is analyzed by numerical modeling and analytical approximation. The nonlinear wave equations are used to provide design guidelines for the audio parametric array. A time domain finite difference code that accurately solves the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear parabolic wave equation is used to predict the response of the parametric array. The time domain code relates the source size and the carrier frequency to the audible signal response including the output level and beamwidth to considering the implementation issues for audio applications of the parametric array, the emphasis is given to the frequency response and distortion. We use the time domain code to find out the optimal parameters that will help produce the parametric array with highest achievable output in terms of the average power within the demodulated signal. Parameters such as primary input frequency, audio source radius and the modulation method are given utmost importance. The output effect of those parameters are demonstrated through the numerical simulation.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.5B
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• pp.559-573
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• 2008

In this study, we newly proposed 3-D nonlinear wave driver utilizing the Navier-Stokes Eq. the numerical integration of which is carried out using SPH (Smoothed Particle Hydrodynamics), an internal wave generation with the source function of Gaussian distribution and an energy absorbing layer. For the verification of new 3-D nonlinear wave driver, we numerically simulate the sloshing problem within a parabolic water basin triggered by a Gaussian hump and uniformly inclined water surface by Thacker (1981). It turns out that the qualitative behavior of sloshing caused by relaxing the external force which makes a free surface convex or uniformly inclined is successfully simulated even though phase error is visible and an inundation height shrinks as numerical simulation more proceeds. For the more severe test, we also simulate the nonlinear shoaling and refraction over uniform beach of wedge shape. It is shown that numerically simulated waves are less refracted than the linear counterpart by Hamiltonian ray theory due to nonlinearity, energy dissipation at the bottom and side walls, energy loss induced by breaking, and the hydraulic jump occurring when breaking waves encounter a down-rush by the preceding wave.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.2
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• pp.43-54
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• 1992

For shallow arches with large dynamic loading, linear analysis is no longer considered as practical and accurate. In this study, a method is presented for the dynamic analysis of shallow arches in which geometric nonlinearity must be considered. A program is developed for the analysis of the nonlinear dynamic behavior and for evaluation of critical buckling loads of shallow arches. Geometric nonlinearity is modeled using Lagrangian description of the motion. The finite element analysis procedure is used to solve the dynamic equation of motion and Newmark method is adopted in the approximation of time integration. A shallow arch subject to radial step loads is analyzed. The results are compared with those from other researches to verify the developed program. The behavior of arches is analyzed using the non-dimensional time, load, and shape parameters. It is shown that geometric nonlinearity should be considered in the analysis of shallow arches and probability of buckling failure is getting higher as arches are getting shallower. It is confirmed that arches with the same shape parameter have the same deflection ratio at the same time parameter when arches are loaded with the same parametric load. In addition, it is proved that buckling of arches with the same shape parameter occurs at the same load parameter. Circular arches, which are under a single or uniform normal load, are analyzed for comparison. A parabolic arch with radial step load is also analyzed. It is verified that the developed program is applicable for those problems.

• Journal of Astronomy and Space Sciences
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• v.14 no.2
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• pp.242-250
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• 1997

The CCD photometric observations of W UMa-type eclipsing binary AB And were made from September 1994 to October 1996. New four primary minimum times were obtained from these observations. The analysis of times of minimum light for AB And confirms other previous studies that the orbital period of AB And have been changing as a form of sinusoidal variation. In this paper, we calculated the new orbital elements with linear and nonlinear quadratic term, and the best fit equation is derived with the assumption that the period variation of AB And changes sinusoidal pattern. From the sinusoidal term of this orbital element, we calculate period variation as 92 years with amplitude of $0.^{d}059$. However this result considering only sinusoidal term, was not satisfied with our recent observations. Thus, by assuming another parabolic period variation with the sinusoidal pattern, we derived the best fit orbital elements. From the quadratic coefficient of this orbital elements, we calculated the secular variation of 0.73 seconds, and from the sinusoidal term, the period variation turned out to be 62.9 years with amplitude of $0.^{d}024$. If we assume only the sinusoidal period variation of AB And, the period has to be decreased within 10 years. However if we consider quadratic term with the sinusoidal period variation of the light elements, the period is expected to be increased. Therefore long-term observations of this binary system are required to confirm this issue.