• Smart Structures and Systems
• /
• 제19권1호
• /
• pp.91-103
• /
• 2017

Generalized fractal dimension is used to detect the presence of partial delamination in a composite laminated beam. The effect of boundary conditions and location of delamination on the fractal dimension curve is studied. Appropriability of higher mode shape data for detection of delamination in the beam is evaluated. It is shown that fractal dimension measure can be used to detect the presence of partial delamination in composite beams. It is found that the torsional mode shape is well suited for delamination detection in beams. First natural frequency of delaminated beam is found to be higher than the healthy beam for certain small and partial width delaminations and some boundary conditions. An explanation towards this counter intuitive phenomenon is provided.

• 한국해안·해양공학회논문집
• /
• 제32권1호
• /
• pp.69-84
• /
• 2020

자연 해빈은 해양환경에 따라 침·퇴적을 반복하며 고 파랑에 의해 해빈이 대규모로 침식되더라도 폭풍이 잦아들고 다시 너울이 우세한 해양환경이 회복되는 경우 점진적으로 복원되며, 이러한 해빈 복원은 경계층 streaming을 통해 이루어진다. 이처럼 경계층 streaming은 그 공학적 가치에도 불구하고 해안에서 가용한 표사의 대부분이 공급되는 쇄파 역에서의 경계층 streaming에 대한 우리의 이해는 아직 상당히 부족하다. 이러한 인식에 기초하여 본 연구에서는 쇄파역 경계층 streaming 수리특성을 살펴보기 위해 단조 해안과 사주를 포함한 해안에서의 천수 과정을 수치모의하였다. 수치 모의는 Spatially filtered Navier-Stokes Eq., LES(Large Eddy Simulation), Dynamic Smagorinsky 난류모형으로 구성된 정교한 수치모형에 기초하여 수행되었으며, 이 과정에서 k-ε 난류모형과 LES Turbulence Closure가 모의결과에 미치는 영향도 함께 살펴보았다. 모의결과 해안공학계에 잘 알려진 k-ε 난류모형의 한계로 인해 wall function에 기반한 k-ε 난류모형의 경우 LES와 비교하면 저면 인근 유속이 다소 과다하게 모의 되었다. 또한, 바닥과 가까운 해역에서의 유속이 바닥의 영향으로부터 비교적 자유로운 상층부에서의 유속보다 우월한 Longuet-Higgins(1957)가 이야기하는 전형적인 경계층 streaming이 천수 초입부에서부터 쇄파 역 깊숙이까지 존재하는 것을 확인하였다. 또한, 주기가 상대적으로 긴 경우 경계층 streaming의 세기와 생성범위는 해안 방향으로 확대되며 이러한 경향은 경계층 streaming이 바닥 인근에서 진행되는 마찰로 인한 파랑에너지손실로 결과되며 주기가 긴 경우 천수 과정이 일찍 시작된다는 사실을 상기하면 충분히 수용 가능해 보이며, Longuet-Higgins(1957)의 해석 해에서도 같은 경향을 확인할 수 있다.

• 한국강구조학회 논문집
• /
• 제14권1호
• /
• pp.23-29
• /
• 2002

거더와 가로보를 포함하는 많은 교량시스템과 콘크리트 상판은 특별직교이방성 판처럼 거동한다. 그런데 Navier나 Levy의 해로 해결할 수 없는 경계조건을 가졌거나, 불규칙 단면을 가진 경에에 해석해를 얻기 것이 매우 어렵다. 더구나 이러한 경우, 고유치 문제에 대한 수치해법은 너무 복잡하다. 그러나 불규칙 단면을 갖는 보와 탑에 대해, 첫 번째 진동모드에 해당하는 고유진동수를 계산하는 방법이 1974년 '김'에 의해 개발되어 발표되었다. 최근에 이 방법은 2차원 문제로 확장되었고 전단변형이 고려된 복합판에 적용되어 왔다. 본 연구에서는 이 방법을 다양한 경계조건을 갖는 특별직교이방성 복합적층판에 적용하여 타당성을 검토하고 그 해석결과를 제시한다.

• Structural Engineering and Mechanics
• /
• 제61권5호
• /
• pp.617-624
• /
• 2017

Piezoelectric nanobeams are used in several nano electromechanical systems. The first step in designing these systems is conducting a vibration analysis. In this research, the free vibration of a piezoelectric nanobeam is analyzed by using the nonlocal elasticity theory. The nanobeam is modeled based on Euler-Bernoulli beam theory. Hamilton's principle is used to derive the equations of motion and also the boundary conditions of the system. The obtained equations of motion are solved by using both Galerkin and the Differential Quadrature (DQ) methods. The clamped-clamped and cantilever boundary conditions are analyzed and the effects of the applied voltage and nonlocal parameter on the natural frequencies and mode shapes are studied. The results show the success of Galerkin method in determining the natural frequencies. The results also show the influence of the nonlocal parameter on the natural frequencies. Increasing a positive voltage decreases the natural frequencies, while increasing a negative voltage increases them. It is also concluded that for the clamped parts of the beam and also other parts that encounter higher values of stress during free vibrations of the beam, anti-nodes in voltage mode shapes are observed. On the contrary, in the parts of the beam that the values of the induced stress are low, the values of the amplitude of the voltage mode shape are not significant. The obtained results and especially the mode shapes can be used in future studies on the forced vibrations of piezoelectric nanobeams based on Galerkin method.

• Structural Engineering and Mechanics
• /
• 제57권5호
• /
• pp.877-895
• /
• 2016

This paper is concerned with the analytical derivation of natural sloshing frequencies of liquid in annular cylindrical tank and its verification by experiment. The whole liquid domain is divided into three simple sub-regions, and the region-wise linearized velocity potentials are derived by the separation of variables. Two sets of matrix equations for solving the natural sloshing frequencies are derived by enforcing the boundary conditions and the continuity conditions at the interfaces between sub-regions. In addition, the natural sloshing frequencies are measured by experiment and the numerical accuracy of the proposed analytical method is verified through the comparison between the analytical and experimental results. It is confirmed that the present analytical method provides the fundamental sloshing frequencies which are in an excellent agreement with the experiment. As well, the effects of the tank radial gap, the bottom flow gap and the liquid fill height on the fundamental sloshing frequency are parametrically investigated.

• Steel and Composite Structures
• /
• 제31권6호
• /
• pp.591-600
• /
• 2019

Based on the energy-variational principle, a coupling vibration analysis model of high-speed railway simply supported beam bridge-track structure system (HSRBTS) was established by considering the effect of shear deformation. The vibration differential equation and natural boundary conditions of HSRBTS were derived by considering the interlayer slip effect. Then, an analytic calculation method for the natural vibration frequency of this system was obtained. By taking two simply supported beam bridges of high-speed railway of 24 m and 32 m in span as examples, ANSYS and MIDAS finite-element numerical calculation methods were compared with the analytic method established in this paper. The calculation results show that two of them agree well with each other, validating the analytic method reported in this paper. The analytic method established in this study was used to evaluate the natural vibration characteristics of HSRBTS under different interlayer stiffness and length of rails at different subgrade sections. The results show that the vertical interlayer compressive stiffness had a great influence on the high-order natural vibration frequency of HSRBTS, and the effect of longitudinal interlayer slip stiffness on the natural vibration frequency of HSRBTS could be ignored. Under different vertical interlayer stiffness conditions, the subgrade section of HSRBTS has a critical rail length, and the critical length of rail at subgrade section decreases with the increase in vertical interlayer compressive stiffness.

• 산업기술연구
• /
• 제16권
• /
• pp.123-129
• /
• 1996

A method of calculating the natural frequency corresponding to the first mode of vibration of beams and tower structures with irregular cross-sections and with arbitrary boundary conditions was developed and reported by D. H. Kim in 1974. In order to obtain the natural frequency by the presented method, the first step to take is to obtain the deflection influence surfaces. In design and analysis of any structure, the first step to be taken is to obtain this deflection influence surfaces. Any method can be used for this purpose. Then using this surfaces, deflections, slopes, moments, shears, and natural frequencies can be obtained by differentiating either the continuous function or discrete function defined at certain points. The merit of the presented method is that the natural frequency can be obtained by the deflection influence surfaces obtaining which is the first step in structural analysis.

• Ocean Systems Engineering
• /
• 제1권4호
• /
• pp.355-372
• /
• 2011

Based on the fully nonlinear velocity potential theory, the liquid sloshing in a three dimensional tank under random excitation is studied. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing scheme, B-spline curve, is applied to both the longitudinal and transverse directions of the tank to eliminate the possible saw-tooth instabilities. When the tank is undergoing one dimensional regular motion of small amplitude, the calculated results are found to be in very good agreement with linear analytical solution. In the simulation, the normal standing waves, travelling waves and bores are observed. The extensive calculation has been made for the tank undergoing specified random oscillation. The nonlinear effect of random sloshing wave is studied and the effect of peak frequency used for the generation of random oscillation is investigated. It is found that, even as the peak value of spectrum for oscillation becomes smaller, the maximum wave elevation on the side wall becomes bigger when the peak frequency is closer to the natural frequency.

• Advances in Computational Design
• /
• 제3권3호
• /
• pp.213-232
• /
• 2018

First time, an exact solution for free vibration of the Levy-type rectangular laminated plate is developed considering the most efficient Zig-Zag theory (ZIGT) and third order theory (TOT). The plate is subjected to hard simply supported boundary condition (Levy-type) along x axis. Using the equilibrium equations and the plate constitutive relations, a set of 12 m first order differential homogenous equations are obtained, containing displacements and stress resultant as primary variables. The natural frequencies of a single-layer isotropic, multi-layer composites and sandwich plates are tabulated for three values of length-to-thickness ratio (S) and five set of boundary conditions and further assessed by comparing with existing literature and recently developed 3D EKM (extended Kantorovich method) solution. It is found that for the symmetric composite plate, TOT produces better results than ZIGT. For antisymmetric and sandwich plates, ZIGT predicts the frequency for different boundary conditions within 3% error with respect to 3D elasticity solution while TOT gives 10% error. But, ZIGT gives better predictions than the TOT concerning the displacement and stress variables.

• Advances in nano research
• /
• 제4권2호
• /
• pp.85-111
• /
• 2016

In this paper, the classical and non-classical boundary conditions effect on free vibration characteristics of functionally graded (FG) size-dependent nanobeams are investigated by presenting a semi analytical differential transform method (DTM) for the first time. Three kinds of mathematical models, namely; power law (P-FGM), sigmoid (S-FGM) and Mori-Tanaka (MT-FGM) distribution are considered to describe the material properties in the thickness direction. The nonlocal Eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. Governing equations are derived through Hamilton's principle and they are solved applying semi analytical differential transform method. The good agreement between the results of this article and those available in literature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as small scale effects, spring constant factors, various material compositions and mode number on the normalized natural frequencies of the FG nanobeams in detail. It is explicitly shown that the vibration of FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.