• 한국해양공학회지
• /
• 제36권2호
• /
• pp.101-107
• /
• 2022

Dean (1965) proposed the use of the root mean square error (RMSE) in the dynamic free surface boundary condition (DFSBC) and kinematic free-surface boundary condition (KFSBC) as an error evaluation criterion for wave theories. There are well known wave theories with RMSE more than 1%, such as Airy theory, Stokes theory, Dean's stream function theory, Fenton's theory, and trochodial theory for deep-water waves. However, none of them can be applied for deep-water breaking waves. The purpose of this study is to provide a closed-form solution for deep-water waves with RMSE less than 1% even for breaking waves. This study is based on a previous study (Shin, 2016), and all flow fields were simplified for deep-water waves. For a closed-form solution, all Fourier series coefficients and all related parameters are presented with Newton's polynomials, which were determined by curve fitting data (Shin, 2016). For verification, a wave in Miche's limit was calculated, and, the profiles, velocities, and the accelerations were compared with those of 5^th-order Stokes theory. The results give greater velocities and acceleration than 5^th-order Stokes theory, and the wavelength depends on the wave height. The results satisfy the Laplace equation, bottom boundary condition (BBC), and KFSBC, while Stokes theory satisfies only the Laplace equation and BBC. RMSE in DFSBC less than 7.25×10^-2% was obtained. The series order of the proposed method is three, but the series order of 5^th-order Stokes theory is five. Nevertheless, this study provides less RMSE than 5^th-order Stokes theory. As a result, the method is suitable for offshore structural design.

• Advances in aircraft and spacecraft science
• /
• 제4권6호
• /
• pp.711-727
• /
• 2017

This article is concerned with a two-dimensional problem of micropolar generalized thermoelasticity for a half-space whose surface is traction-free and the conductive temperature at the surface of the half-space is known. Theory of two-temperature generalized thermoelasticity with phase lags using the normal mode analysis is used to solve the present problem. The formulas of conductive and mechanical temperatures, displacement, micro-rotation, stresses and couple stresses are obtained. The considered quantities are illustrated graphically and their behaviors are discussed with suitable comparisons. The present results are compared with those obtained according to one temperature theory. It is concluded that both conductive heat wave and thermodynamical heat wave should be separated. The two-temperature theory describes the behavior of particles of elastic body more real than one-temperature theory.

• 한국해양공학회지
• /
• 제10권3호
• /
• pp.96-104
• /
• 1996

Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.

• International Journal of Naval Architecture and Ocean Engineering
• /
• 제9권2호
• /
• pp.160-176
• /
• 2017

The interaction of focused wave groups with a vertical wall is investigated based on the second order potential theory. The NewWave theory, which represents the most probable surface elevation under a large crest, is adopted. The analytical solutions of the surface elevation, velocity potential and wave force exerted on the vertical wall are derived, up to the second order. Then, a parametric study is made on the interaction between nonlinear focused wave groups and a vertical wall by considering the effects of angles of incidence, wave steepness, focal positions, water depth, frequency bandwidth and the peak lifting factor. Results show that the wave force on the vertical wall for obliquely-incident wave groups is larger than that for normally-incident waves. The normalized peak crest of wave forces reduces with the increase of wave steepness. With the increase of the distance of focal positions from the vertical wall, the peak crest of surface elevation, although fluctuates, decreases gradually. Both the normalized peak crest and adjacent crest and trough of wave forces become larger for shallower water depth. For focused wave groups reflected by a vertical wall, the frequency bandwidth has little effects on the peak crest of wave elevation or forces, but the adjacent crest and trough become smaller for larger frequency bandwidth. There is no significant change of the peak crest and adjacent trough of surface elevation and wave forces for variation of the peak lifting factor. However, the adjacent crest increases with the increase of the peak lifting factor.

• 한국전자통신학회논문지
• /
• 제5권3호
• /
• pp.281-287
• /
• 2010

본 논문은 matlab을 개발툴로 사용하여 해양파도의 표면운동의 해석에 대한 것이다. 해양의 파도 및 바다표면파에 대하여 이론에 근거하여 해석에 대하여 연구하였다. 또한 3차원 바다파도와 2차원 바다파도의 운동을 Matlab을 이용하여 시뮬레이션하고 각각의 운동 형태를 시뮬레이션을 통하여 분석하고 그 결과를 고찰하였다.

• 한국철도학회:학술대회논문집
• /
• 한국철도학회 2011년도 정기총회 및 추계학술대회 논문집
• /
• pp.2632-2634
• /
• 2011

In the Structural Health Monitoring field, the piezoelectric elements are bonded the surface of the structures for generating the guided wave. For this reason, the structures become two-layer beam. It is very important to know precisely the dynamic characteristic of structures and also predict precisely the wave propagation in structures. Because wave propagation is very useful to analysis the dynamic characteristic of structures. In this paper, the governing equations of motion are derived from Hamilton's principle by applying the Timoshenko beam theory and Mindlin-Herrmann rod theory at the first. and then the wave propagations in a composite beams with a surface-bonded piezoelectric are examined.

• Journal of Advanced Research in Ocean Engineering
• /
• 제2권1호
• /
• pp.1-11
• /
• 2016

The objective of this paper is to present an analytical solution in deep water waves and verify the validity of the theory (Shin, 2015). Hence this is a follow-up to Shin (2015). Instead of a variational approach, another approach was considered for a more accurate assessment in this study. The products of two coefficients were not neglected in this study. The two wave profiles from the KFSBC and DFSBC were evaluated at N discrete points on the free-surface, and the combination coefficients were determined for when the two curves pass the discrete points. Thus, the solution satisfies the differential equation (DE), bottom boundary condition (BBC), and the kinematic free surface boundary condition (KFSBC) exactly. The error in the dynamic free surface boundary condition (DFSBC) is less than 0.003%. The wave theory was simplified based on the assumption tanh $D{\approx}1$ in this paper. Unlike the perturbation method, the results are possible for steep waves and can be calculated without iteration. The result is very simple compared to the 5th Stokes' theory. Stokes' breaking-wave criterion has been checked in this study.

• 한국수자원학회:학술대회논문집
• /
• 한국수자원학회 2005년도 학술발표회(2)
• /
• pp.842-845
• /
• 2005

A method for the numerical simulation of two-dimensional free-surface flow resulting from the propagation of regular gravity waves over topography with arbitrary bottom shape is presented. The method is based on the numerical solution of the Euler equations subject to the fully nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow conditions using a hybrid finite-differences and spectral-method scheme. The formulation includes a boundary-fitted transformation, and is suitable for extension to incorporate large-eddy simulation (LES) and large-wave simulation (LWS) terms for turbulence and breaking wave modeling, respectively. Results are presented for the simulation of the free-surface flow over two different bottom topographies, with constant slope values of 1:10 and 1:20, two different inflow wave lengths and two different inflow wave heights. An absorption outflow zone is utilized and the results indicate minimum wave reflection from the outflow boundary. Over the bottom slope, lengths of waves in the linear regime are modified according to linear theory dispersion, while wave heights remain more or less unchanged. For waves in the nonlinear regime, wave lengths are becoming shorter, while the free surface elevation deviates from its initial sinusoidal shape.

• International Journal of Naval Architecture and Ocean Engineering
• /
• 제4권3호
• /
• pp.281-290
• /
• 2012

Hydrodynamic analysis of a surface-piercing body with an open chamber was performed with incident regular waves and forced-heaving body motions. The floating body was simulated in the time domain using a 2D fully nonlinear numerical wave tank (NWT) technique based on potential theory. This paper focuses on the hydrodynamic behavior of the free surfaces inside the chamber for various input conditions, including a two-input system: both incident wave profiles and forced body velocities were implemented in order to calculate the maximum surface elevations for the respective inputs and evaluate their interactions. An appropriate equivalent linear or quadratic viscous damping coefficient, which was selected from experimental data, was employed on the free surface boundary inside the chamber to account for the viscous energy loss on the system. Then a comprehensive parametric study was performed to investigate the nonlinear behavior of the wave-body interaction.

• Structural Engineering and Mechanics
• /
• 제90권2호
• /
• pp.209-218
• /
• 2024

The present paper is focused on the study of the propagation of plane waves in thermoelastic media under a modified Green-Lindsay (MG-L) model having the influence of non-local and two temperature. The problem is formulated for the considered model in dimensionless form and is explained by using the reflection phenomenon. The plane wave solution of these equations indicates the existence of three waves namely Longitudinal waves (LD-Wave), Thermal waves (T-wave), and Shear waves (SV-wave) from a stress-free surface. The variation of amplitude ratios is computed analytically and depicted graphically against the angle of incidence to elaborate the impact of non-local, two temperature, and different theories of thermoelasticity. Some particular cases of interest are also deduced from the present investigation. The present study finds applications in a wide range of problems in engineering and sciences, control theory, vibration mechanics, and continuum mechanics.