• Nuclear Engineering and Technology
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• 제41권3호
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• pp.335-346
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• 2009

This paper deals with a hydroelastic vibration analysis of two rectangular plates partially coupled with a liquid, which is bounded by two plates and two rigid side walls. The wet displacement of each plate is assumed to be a combination of the modal functions of a dry uniform beam with a clamped boundary condition. As the liquid is assumed to be an ideal liquid, the displacement potential satisfying the Laplace equation is determined so that the liquid boundary conditions can meet the requirements at the rigid surfaces and the free liquid surface. The wet dynamic modal functions of each plate are expanded by using the finite Fourier transform to obtain an appropriate form of the compatibility requirement along the contacting surfaces between the plates and the liquid. The liquid-coupled natural frequencies of the plates are derived by using the Rayleigh-Ritz method. Finite element analyses using commercial software are carried out to verify the proposed theory. It is observed that the theoretical method agrees excellently with the three-dimensional finite element analyses results. The effects of the liquid depth and the liquid thickness on the normalized natural frequencies are investigated to identify the dynamic characteristics of the liquid coupled system.

• Structural Engineering and Mechanics
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• 제40권5호
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• pp.665-688
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• 2011

This paper presents a theoretical analysis for the free vibration of rectangular tanks partially filled with an ideal liquid. Wet dynamic displacements of the tanks are approximated by combining the orthogonal polynomials satisfying the boundary conditions, since the rectangular tanks are composed of four rectangular plates. The classical boundary conditions of the tanks at the top and bottom ends are considered, such as clamped, simply supported, and clamped-free boundary conditions. As the facing rectangular plates are assumed to be geometrically and structurally identical, the vibration modes of the facing plates of the tanks can be divided into two categories: symmetric and antisymmetric modes with respect to the planes passing through the center of the tanks and perpendicular to the free liquid surface. The liquid displacement potentials satisfying the Laplace equation and liquid boundary conditions are derived, and the wet dynamic modal functions of a quarter of the tanks can be expanded by the finite Fourier transform for compatibility requirements along the contacting surfaces between the tanks and liquid. An eigenvalue problem is derived using the Rayleigh-Ritz method. Consequently, the wet natural frequencies of the rectangular tanks can be extracted. The proposed analytical method is verified by observing an excellent agreement with three-dimensional finite element analysis results. The effects of the liquid level and boundary condition at the top and bottom edges are investigated.

• 한국지진공학회논문집
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• 제2권1호
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• pp.23-34
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• 1998

연약한 지반위에 기초한 유연한 구형 액체 저장탱크의 Rocking 운동에 대한 3차원 지진응답을 규명하기 위해서 동적 유체-구조 물-지반 계의 상호작용 해석방법을 개발하였다. 수평방향 병진 운동과 Rocking 운동을 받는 3차원의 구형 탱크의 운동 지배방정식을 Rayleigh-Ritz 방법을 적용하여 유도하였고 기반암위 토층의 표면에 놓인 강체 기초의 동적 강성행렬과 유체-구조물 계의 지배방정식을 결합하여 계산하였다.

• Steel and Composite Structures
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• 제31권3호
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• pp.233-242
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• 2019

Early detection of damage bonding state such as insufficient bonding strength and interface partial contact defect for the explosive clad pipe is crucial in order to avoid sudden failure and even catastrophic accidents. A generalized and efficient model of the explosive clad pipe can reveal the relationship between bonding state and vibration characteristics, and provide foundations and priory knowledge for bonding state detection by signal processing technique. In this paper, the slender explosive clad pipe is regarded as two parallel elastic beams continuously joined by an elastic layer, and the elastic layer is capable to describe the non-uniform bonding state. By taking the characteristic beam modal functions as the admissible functions, the Rayleigh-Ritz method is employed to derive the dynamic model which enables one to consider inhomogeneous system and any boundary conditions. Then, the proposed model is validated by both numerical results and experiment. Parametric studies are carried out to investigate the effects of bonding strength and the length of partial contact defect on the natural frequency and forced response of the explosive clad pipe. A potential method for identifying the bonding quality of the explosive clad pipe is also discussed in this paper.

• 대한조선학회논문집
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• 제29권1호
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• pp.158-172
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• 1992

대형구조물의 국부구조계를 구성하는 후판, 선체이중저구조와 같은 복판팬널등의 진동문제에 있어서 전단변형 및 회전관성효과가 매우 크므로 정확한 진동해석을 위해서는 이들 구조계를 상기 효과를 고려한 Mindlin판유추 구조계로 취급하여야 한다. 또한, 이들 구조계의 실제 경계조건은 일반적으로 단순지지와 고정의 중간상태이므로 경계조건을 회전에 대한 탄성구속으로 다룰 필요가 있다. 그러나 4변모두 단순지지 경계조건을 갖는 Mindlin판을 제외하고는 엄밀해를 구하기 어려워 근사적 방법의 사용이 불가피한데, 한 방법으로 Rayleigh-Ritz 방법이 널리 이용된다. Rayleigh-Ritz 방법에 의한 Mindlin판유추 구조계의 진동해석에 있어서 진동파형가정함수로서 통상 Timoshenko보함수가 이용된다. 이 경우 전단변형의 효과가 고려되어야 하므로 횡방향처짐 및 굽힘회전각에 대한 2개의 함수계가 도입되어야 하므로 실제 연산이 Euler보함수를 이용한 박판유추 구조계의 진동해석 때 보다도 훨씬 더 복잡하다. 따라서, 본 논문에서는 이러한 연산의 복잡성을 줄이기 위해 진동파형가정함수로서 Timoshenko보함수 성질을 갖는 다항식 도출방안을 제시하였고, 이를 이용하여 주변경계조건이 회전에 대해 탄성구속된 Mindlin판유추 구조계의 진동해석 및 감도해석을 정식화하여, 등방성 후판 및 실선이중저구조의 1/8축척 모델을 대상으로 일련의 수치계산을 수행하여 이의 정확도 및 효율성을 검증하였다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2005년도 창립60주년 기념 추계 학술대회
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• pp.191.2-191.2
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• 2005

• Structural Engineering and Mechanics
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• 제67권4호
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• pp.417-425
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• 2018

The main aim of this paper is to investigate the bending of Euler-Bernouilli nano-beams made of bi-directional functionally graded materials (BDFGMs) using Eringen's non-local elasticity theory in the integral form with compare the differential form. To the best of the researchers' knowledge, in the literature, there is no study carried out into integral form of Eringen's non-local elasticity theory for bending analysis of BDFGM Euler-Bernoulli nano-beams with arbitrary functions. Material properties of nano-beam are assumed to change along the thickness and length directions according to arbitrary function. The approximate analytical solutions to the bending analysis of the BDFG nano-beam are derived by using the Rayleigh-Ritz method. The differential form of Eringen's non-local elasticity theory reveals with increasing size effect parameter, the flexibility of the nano-beam decreases, that this is unreasonable. This problem has been resolved in the integral form of the Eringen's model. For all boundary conditions, it is clearly seen that the integral form of Eringen's model predicts the softening effect of the non-local parameter as expected. Finally, the effects of changes of some important parameters such as material length scale, BDFG index on the values of deflection of nano-beam are studied.

• Steel and Composite Structures
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• 제4권4호
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• pp.281-301
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• 2004

The paper begins by presenting a unified variational approach to the lateral-torsional buckling (LTB) analysis of doubly symmetric prismatic and tapered thin-walled beams with open cross-sections, which accounts for the influence of the pre-buckling deflections. This approach (i) extends the kinematical assumptions usually adopted for prismatic beams, (ii) consistently uses shell membrane theory in general coordinates and (iii) adopts Trefftz's criterion to perform the bifurcation analysis. The proposed formulation is then applied to investigate the influence of the pre-buckling deflections on the LTB behaviour of prismatic and web-tapered I-section simply supported beams and cantilevers. After establishing an interesting analytical result, valid for prismatic members with shear centre loading, several elastic critical moments/loads are presented, discussed and, when possible, also compared with values reported in the literature. These numerical results, which are obtained by means of the Rayleigh-Ritz method, (i) highlight the qualitative differences existing between the LTB behaviours of simply supported beams and cantilevers and (ii) illustrate how the influence of the pre-buckling deflections on LTB is affected by a number of factors, namely ($ii_1$) the minor-to-major inertia ratio, ($ii_2$) the beam length, ($ii_3$) the location of the load point of application and ($ii_4$) the bending moment diagram shape.

• 한국구조물진단유지관리공학회 논문집
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• 제18권1호
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• pp.150-159
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• 2014

본 논문은 초기하중을 받는 직사각형판 및 역대칭 Angle-Ply 적층판의 좌굴 및 진동특성을 무재하시의 고유진동수를 이용하여 산정하는 간편법을 제시하였다. 마주보는 두변이 단순지지된 직사각형판의 운동방정식은 곡률항을 고려한 Mindlin 판이론과 에너지원리를 이용한 Rayleigh-Ritz법을 이용하여 유도하였다. 초기응력을 받는 직사각형판의 무차원화 고유진동수, 임계좌굴계수 및 동적불안정영역 문제들을 무재하시의 무차원화 고유진동수로서 각각의 특성을 정립하였다. 본 연구에서 제안한 진동특성에 관한 간편산정식의 타당성과 사용성을 입증하기 위해 수치예를 들어 검토하였다.

• 한국재난정보학회 논문집
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• 제11권4호
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• pp.527-533
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• 2015

본 논문은 초기하중을 받는 역대칭 Cross-Ply 원통쉘의 동적특성을 고유진동수를 이용하여 해석하였다. 마주보는 두변이 단순지지된 적층 원통쉘의 운동방정식은 곡률항을 고려한 Mindlin 쉘이론과 에너지원리를 이용한 Rayleigh-Ritz법을 이용하여 유도하였다. 초기응력을 받는 적층쉘의 고유진동수, 임계좌굴계수 및 동적불안정영역 문제들을 무재하시의 무차원화 고유진동수로서 각각의 특성을 정립하였다. 본 연구에서 제안한 진동특성에 관한 간편산정식의 타당성과 사용성을 입증하기 위해 수치예를 들어 검토하였다.