• 제목/요약/키워드: Parabolic Equations

검색결과 255건 처리시간 0.027초

Analysis of Wave Transmission Characteristics on the TTP Submerged Breakwater Using a Parabolic-Type Linear Wave Deformation Model

  • Jeong, Jin-Hwan;Kim, Jin-Hoon;Lee, Jung-Lyul
    • 한국해양공학회지
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    • 제35권1호
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    • pp.82-90
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    • 2021
  • Owing to the advantages of assuring the best views and seawater exchange, submerged breakwaters have been widely installed along the eastern coast of Korea in recent years. It significantly contributes to promoting the advancement of shorelines by partially inhibiting incident wave energy. Observations were carried out by a pressure-type wave gauge in the Bongpo Beach to evaluate the coefficients of wave transmission via a submerged breakwater, and the results obtained were compared with those of existing conventional equations on the transmission coefficient derived from hydraulic experiments. After reviewing the existing equations, we proposed a transmission coefficient equation in terms of an error function. Although it exhibited robust relationships with the crest height and breaking coefficient, deviations from the observed data were evident and considered to be triggered by the difference in the incident wave climate. Therefore, in this study, we conducted a numerical experiment to verify the influence of wave period on the coefficients of wave transmission, in which we adopted a parabolic-type mild-slope equation model. Consequently, the deviation from calculated results appears to practically cover all deviation range in the observed data. The wave period and direction of the incident wave increased, the transmission coefficient decreased, and the wave direction was determined to demonstrate a relatively significant influence on the transmission coefficient. It was inferred that this numerical study is expected to be used practically in evaluating the design achievement of the submerged breakwater, which is adopted as a countermeasure to coastal beach erosion.

약한 충격파의 포커싱 현상에 관한 수치해석적 연구 (A Computational Study of the Focusing Phenomenon of Weak Shock Wave)

  • 권용훈;김희동
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2002년도 학술대회지
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    • pp.169-172
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    • 2002
  • When a plane shockwave reflects ken a concave wall, it is focused at a certain location, resulting in extremely high local pressure and temperature. This focusing is due to a nonlinear phenomenon of shock wave. The focusing phenomenon has been extensively applied to many diverse folds of engineering and medical treatment as well. In the current study, the focusing of shock wave over a reflector is numerically investigated using a CFD method. The Harten-Yee total variation diminishing (TVD) scheme is used to solve the unsteady, two-dimensional, compressible, Euler equations. The incident shock wave Mach number $M_{s}\;of\;1.1{\~}l.3$ is applied to the parabolic reflectors with several different depths. Detailed focusing characteristics of the shock wave are investigated in terms of peak pressure, gasdynamic and geometrical foci. The results obtained are compared with the previous experimental results. The results obtained show that the peak pressure of shock wave focusing and its location strongly depend on the magnitude of the incident shock wave and depth of parabolic reflector. It is also found that depending up on the depth of parabolic reflector, the weak shock wave focusing process can classified into three distinct patterns : the reflected shock waves do not intersect each other before and after focusing, the reflected shock waves do not intersect each other before focusing, but intersect after focusing, and the reflected shock waves intersect each other before and after focusing. The predicted Schlieren images represent the measured shock wave focusing with a good accuracy.

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포물선형 완경사 방정식에 의한 회절현상의 수치해석 (Numerical Analysis of Diffraction Using Parabolic Mild-Slope Equation)

  • 김상욱;손민우;백경오
    • 한국수자원학회:학술대회논문집
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    • 한국수자원학회 2006년도 학술발표회 논문집
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    • pp.1914-1918
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    • 2006
  • 나날이 해안의 개발이 증대되어지고 있는 시점에, 안전한 항만 구조물의 설치와 그와 관련된 설비의 중요성이 증폭되고 있다. 특히 항내의 안전을 위해서 방파제의 건설이 필요한데 이에 따른 파의 회절현상을 이해함으로써 항내에서의 파고 등을 예측하는데 도움이 되리라 생각한다. 파의 변형을 예측하기 위해서는 수치적인 방법인 FDM을 사용하여 포물선형 완경사방정식을 차분함으로써 해를 얻을 수 있었고, 적용대상으로서 개구부가 있는 방파제와 반무한방파제를 선정 하였다. 각각 파의 입사각을 $0^{\circ},\;30^{\circ},\;60^{\circ}$로 하여 이 후 파의 변형을 예측하였고, 이의 Diffraction Coefficient와 Amplitude 결과를 도시한 후 Penny와 Price의 해 및 Memos의 해와 비교하였다.

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A simple analytical model for free vibration and buckling analysis of orthotropic rectangular plates

  • Sellam, Souad;Draiche, Kada;Tlidji, Youcef;Addou, Farouk Yahia;Benachour, Abdelkader
    • Structural Engineering and Mechanics
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    • 제75권2호
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    • pp.157-174
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    • 2020
  • In the present paper, a simple analytical model is developed based on a new refined parabolic shear deformation theory (RPSDT) for free vibration and buckling analysis of orthotropic rectangular plates with simply supported boundary conditions. The displacement field is simpler than those of other higher-order theories since it is modeled with only two unknowns and accounts for a parabolic distribution of the transverse shear stress through the plate thickness. The governing differential equations related to the present theory are obtained from the principle of virtual work, while the solution of the eigenvalue problem is achieved by assuming a Navier technique in the form of a double trigonometric series that satisfy the edge boundary conditions of the plate. Numerical results are presented and compared with previously published results for orthotropic rectangular plates in order to verify the precision of the proposed analytical model and to assess the impacts of several parameters such as the modulus ratio, the side-to-thickness ratio and the geometric ratio on natural frequencies and critical buckling loads. From these results, it can be concluded that the present computations are in excellent agreement with the other higher-order theories.

단면적이 일정한 직사각형 중공단면을 갖는 아치의 자유진동 (Free Vibrations of Arches with Rectangular Hollow Section having Constant Area)

  • 이태은;이병구;박광규
    • 한국전산구조공학회논문집
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    • 제21권4호
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    • pp.357-364
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    • 2008
  • 본 논문은 단면적이 일정한 직사각형 중공단면을 갖는 아치의 자유진동에 관한 연구이다. 아치의 자유진동을 지배하는 미분방정식을 극좌표계에서 유도하였으며, 이 미분방정식에는 회전관성효과를 고려하였다. 본 연구에서는 원호아치에 비해 구조적 안정성이 우수한 포물선형 아치를 대상아치의 선형으로 결정하였으며, 고정-고정, 고정-회전, 회전-회전의 단부조건을 고려하였다. 미분방정식을 효율적으로 해석하여 정확한 고유진동수를 산정할 수 있는 수치해석 알고리즘을 개발하고, 문헌과 본 연구의 결과를 비교하여 본 연구에서 유도된 이론식 및 수치해석 과정의 타당성을 검증하였으며, 단면폭비, 두께비 및 형상비 등과 같은 제 변수 변화에 따른 무차원 고유진동수의 변화를 고찰하였다.

직립벽을 따른 연파의 수리 및 수치실험 (Hydraulic and Numerical Experiments of Stem Waves along a Vertical Wall)

  • 이종인;윤성범
    • 대한토목학회논문집
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    • 제26권4B호
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    • pp.405-412
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    • 2006
  • 본 연구에서는 직립벽을 따른 규칙파의 연파특성을 평면수조를 이용한 수리실험과 포물형근사식을 이용한 수치해석을 통해 검토하였다. 본 연구는 파랑의 비선형성이 연파의 전파특성에 미치는 영향을 검토하는 것으로서 수리실험결과와 수치해석 결과가 잘 일치함을 알 수 있었다. 본 연구로부터 입사각이 작아지고 입사파의 비선형성이 증가할수록 연파의 파고는 감소하고, 연파의 폭은 증가함을 알 수 있었다.

A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates

  • Karami, Behrouz;Janghorban, Maziar;Shahsavari, Davood;Tounsi, Abdelouahed
    • Steel and Composite Structures
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    • 제28권1호
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    • pp.99-110
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    • 2018
  • In this paper, a new size-dependent quasi-3D plate theory is presented for wave dispersion analysis of functionally graded nanoplates while resting on an elastic foundation and under the hygrothermaal environment. This quasi-3D plate theory considers both thickness stretching influences and shear deformation with the variations of displacements in the thickness direction as a parabolic function. Moreover, the stress-free boundary conditions on both sides of the plate are satisfied without using a shear correction factor. This theory includes five independent unknowns with results in only five governing equations. Size effects are obtained via a higher-order nonlocal strain gradient theory of elasticity. A variational approach is adopted to owning the governing equations employing Hamilton's principle. Solving analytically via Fourier series, these equations gives wave frequencies and phase velocities as a function of wave numbers. The validity of the present results is examined by comparing them with those of the known data in the literature. Parametric studies are conducted for material composition, size dependency, two parametric elastic foundation, temperature and moisture differences, and wave number. Some conclusions are drawn from the parametric studies with respect to the wave characteristics.

최소 위상 오차를 갖는 곡선 배열안테나용 Rotman 렌즈의 설계 (Design of Rotman Lens for Curved Array Antenna with Minimal Phase Error)

  • 박주래;박동철
    • 한국전자파학회논문지
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    • 제25권10호
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    • pp.1077-1086
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    • 2014
  • 컨포멀 배열에 적용할 수 있는 곡선 배열안테나용 Rotman 렌즈의 설계 방법을 제안한다. 본 논문에서는 곡선 배열안테나와 연동하여 Rotman 렌즈의 평행판 영역에 존재하는 배열 포트의 위치와, 배열 포트와 배열안테나 소자를 연결하는 전송선의 길이를 구하는 설계식을 유도하고, 이 설계식을 바탕으로 빔 곡선 최적화 절차와 재초점 절차를 통하여 위상 오차를 최소화하고 있다. 제안된 설계식과 설계 절차에 의해 설계된 Rotman 렌즈는 정확히 3초점을 보유한 채 직선 배열안테나뿐만 아니라, 원곡선, 포물선, V자형 곡선 등의 오목하거나 볼록한 배열안테나를 급전할 수 있으며, 최소의 위상 오차를 나타내고 있다.

임의선형을 갖는 아치의 자유진동 (Free Vibration of Arbitrary Shaped Arches)

  • 이태은;신성철;이병구
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2004년도 추계학술대회논문집
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    • pp.526-529
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    • 2004
  • Arches are one of the most important basic structural units as well as the beams, columns and plates. Most complicated structures consist of only these basic units and therefore it is very attractive research subject to analysis both the static and dynamic behavior of such units including the arches. This study deals with the free vibration of arbitrary shaped arches. In order to obtain the exactly arch shape, which surveyed (x, y) of neutral axis of arbitrary shaped arches are compared to various shape of arch: circular, parabolic, sinusoidal, elliptic, spiral and cartenary. The differential equations governing free vibrations of arches are merely adopted in the open literature rather than deriving the equations in this study. The Taylor series method is used as the numerical differential scheme. The Runge-Kutta method and the Regula-Falsi method, respectively, are used to integrate the governing differential equations and to compute the natural frequencies It is expected that results obtained herein can be practically utilized in the fields of vibration control.

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Static stability and of symmetric and sigmoid functionally graded beam under variable axial load

  • Melaibari, Ammar;Khoshaim, Ahmed B.;Mohamed, Salwa A.;Eltaher, Mohamed A.
    • Steel and Composite Structures
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    • 제35권5호
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    • pp.671-685
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    • 2020
  • This manuscript presents impacts of gradation of material functions and axial load functions on critical buckling loads and mode shapes of functionally graded (FG) thin and thick beams by using higher order shear deformation theory, for the first time. Volume fractions of metal and ceramic materials are assumed to be distributed through a beam thickness by both sigmoid law and symmetric power functions. Ceramic-metal-ceramic (CMC) and metal-ceramic-metal (MCM) symmetric distributions are proposed relative to mid-plane of the beam structure. The axial compressive load is depicted by constant, linear, and parabolic continuous functions through the axial direction. The equilibrium governing equations are derived by using Hamilton's principles. Numerical differential quadrature method (DQM) is developed to discretize the spatial domain and covert the governing variable coefficients differential equations and boundary conditions to system of algebraic equations. Algebraic equations are formed as a generalized matrix eigenvalue problem, that will be solved to get eigenvalues (buckling loads) and eigenvectors (mode shapes). The proposed model is verified with respectable published work. Numerical results depict influences of gradation function, gradation parameter, axial load function, slenderness ratio and boundary conditions on critical buckling loads and mode-shapes of FG beam structure. It is found that gradation types have different effects on the critical buckling. The proposed model can be effective in analysis and design of structure beam element subject to distributed axial compressive load, such as, spacecraft, nuclear structure, and naval structure.