• 소음진동
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• 제9권5호
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• pp.1019-1028
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• 1999

Free vibration characteristics of cantilevered laminated composite beams with a transverse non0propagating open carck are investigated. In the present analysis a special ply-angle distribution referred to as asymmetric stiffness configuration inducing the elastic coupling between chord-wise bending and extension is considered. The open crack is modelled as an equivalent rotational spring whose spring constant is calculated on the basis of fracture mechanics of composite material structures. Governing equations of a composite beam with a open crack are derived via Hamilton's Principle and Timoshenko beam theory encompassing transverse shear and rotary inertia effect. the effects of various parameters such as the ply angle, fiber volume fraction, crack depth, crack position and transverse shear on the free vibration characteristics of the beam with a crack is highlighted. The numerical results show that the natural frequencies obtained from Timoshenko beam theory are always lower than those from Euler beam theory. The presence of intrinsic cracks in anisotropic composite beams modifies the flexibility and in turn free vibration characteristics of the structures. It is revealed that non-destructive crack detection is possible by analyzing the free vibration responses of a cracked beam.

• 대한토목학회논문집
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• 제2권3호
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• pp.75-86
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• 1982

본 연구에서는 3절점, 6자유도를 갖는, 종래의 Timoshenko 보 이론에 근거한 깊은 보(Thick beam) 요소(DB6)와 3절점, 7자유도를 갖는 3차 축방향변위를 가정한 고차 보 요소(DB7)의 3차원 연속체로부터의 Degeneration을 보여 주고 있다. DB6 보 요소는 전단변형률의 비살제적인 선형분포를 보완하기 위하여 전단계수(shear coefficient)를 도입하고 있는 반면 고차 DB7 보 요소는 보다 실제적인 전단변형률의 2차분포를 가정하고 있다. 이 들 두 보 요소를 이용하여 계산된 해(解)는 Timoshenko 방정식의 해(解), 얕은 보(Thin beam)의 해(解) 및 다른 여러 보 요소들의 해(解)와 비교된다. 본 연구의 결과는 고차 DB7 보 요소가 보의 정력화적 해석이나 자유진동 해석에 있어서 다른 보 요소들에 비해 월등히 정확함을 보여주고 있다.

• Advances in nano research
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• 제17권3호
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• pp.275-284
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• 2024

In this article, a nonlocal stress-strain elasticity theory on the vibration analysis of Timoshenko sandwich beam theory with symmetric and asymmetric distributions of porous core and functionally graded material facesheets is introduced. According to nonlocal elasticity Eringen's theory (nonlocal stress elasticity theory), the stress at a reference point in the body is dependent not only on the strain state at that point, but also on the strain state at all of the points throughout the body; while, according to a new nonlocal strain elasticity theory, the strain at a reference point in the body is dependent not only on the stress state at that point, but also on the stress state at all of the points throughout the body. Also, with combinations of two concepts, the nonlocal stress-strain elasticity theory is defined that can be actual at micro/nano scales. It is concluded that the natural frequency decreases with an increase in the nonlocal stress parameter; while, this effect is vice versa for nonlocal strain elasticity, because the stiffness of Timoshenko sandwich beam decreases with increasing of the nonlocal stress parameter; in which, the nonlocal strain parameter leads to increase the stiffness of structures at micro/nano scale. It is seen that the natural frequency by considering both nonlocal stress parameter and nonlocal strain parameter is higher than the nonlocal stress parameter only and lower for a nonlocal strain parameter only.

• Structural Monitoring and Maintenance
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• 제4권2호
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• pp.153-173
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• 2017

An improved method is presented to estimate the axial force of a bar member with vibrational measurements based on modified Timoshenko beam theory. Bending stiffness effects, rotational inertia, shear deformation, rotational inertia caused by shear deformation are all taken into account. Axial forces are estimated with certain natural frequency and corresponding mode shape, which are acquired from dynamic tests with five accelerometers. In the paper, modified Timoshenko beam theory is first presented with the inclusion of axial force and rotational inertia effects. Consistent mass and stiffness matrices for the modified Timoshenko beam theory are derived and then used in finite element simulations to investigate force identification accuracy under different boundary conditions and the influence of critical axial force ratio. The deformation coefficient which accounts for rotational inertia effects of the shearing deformation is discussed, and the relationship between the changing wave speed and the frequency is comprehensively examined to improve accuracy of the deformation coefficient. Finally, dynamic tests are conducted in our laboratory to identify progressive axial forces of a steel plate and a truss structure respectively. And the axial forces identified by the proposed method are in good agreement with the forces measured by FBG sensors and strain gauges. A significant advantage of this axial force identification method is that no assumption on boundary conditions is needed and excellent force identification accuracy can be achieved.

• Coupled systems mechanics
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• 제7권1호
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• pp.27-42
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• 2018

Behavior of soil is usually described with continuum type of failure models such as Mohr-Coulomb or Drucker-Prager model. The main advantage of these models is in a relatively simple and efficient way of predicting the main tendencies and overall behavior of soil in failure analysis of interest for engineering practice. However, the main shortcoming of these models is that they are not able to capture post-peak behavior of soil nor the corresponding failure modes under extreme loading. In this paper we will significantly improve on this state-of-the-art. In particular, we propose the use of a discrete beam lattice model to provide a sharp prediction of inelastic response and failure mechanisms in coupled soil-foundation systems. In the discrete beam lattice model used in this paper, soil is meshed with one-dimensional Timoshenko beam finite elements with embedded strong discontinuities in axial and transverse direction capable of representing crack propagation in mode I and mode II. Mode I relates to crack opening, and mode II relates to crack sliding. To take into account material heterogeneities, we determine fracture limits for each Timoshenko beam with Gaussian random distribution. We compare the results obtained using the discrete beam lattice model against those obtained using the modified three-surface elasto-plastic cap model.

• Advances in nano research
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• 제4권1호
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• pp.51-64
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• 2016

This paper investigates the effects of thermal load and shear force on the buckling of nanobeams. Higher-order shear deformation beam theories are implemented and their predictions of the critical buckling load and post-buckled configurations are compared to those of Euler-Bernoulli and Timoshenko beam theories. The nonlocal Eringen elasticity model is adopted to account a size-dependence at the nano-scale. Analytical closed form solutions for critical buckling loads and post-buckling configurations are derived for proposed beam theories. This would be helpful for those who work in the mechanical analysis of nanobeams especially experimentalists working in the field. Results show that thermal load has a more significant impact on the buckling behavior of simply-supported beams (S-S) than it has on clamped-clamped (C-C) beams. However, the nonlocal effect has more impact on C-C beams that it does on S-S beams. Moreover, it was found that the predictions obtained from Timoshenko beam theory are identical to those obtained using all higher-order shear deformation theories, suggesting that Timoshenko beam theory is sufficient to analyze buckling in nanobeams.

• Structural Engineering and Mechanics
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• 제10권3호
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• pp.197-209
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• 2000

The effects of weight and axial inertia of a beam are taken into account for studying the nonlinear vibration of the Timoshenko beam due to external loads. The combination of Galerkins method and Runge-Kutta method are employed to obtain the dynamic responses of the beam. A concentrated force and a two-axle vehicle traversing on the beam are taken as two examples to investigate the response characteristics of the beam. Results show that the effect of axial inertia of the beam increases the fundamental period of the beam. Further, both the dynamic deflection and the dynamic moment of the beam obtained with including the effect of axial inertia of the beam are greater than those of the beam without including that effect of the beam.

• 한국강구조학회 논문집
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• 제18권3호
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• pp.349-359
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• 2006

본 연구에서는 직교좌표계에 근거한 적층복합 I형 박벽보의 유한요소 해석을 위한 새로운 블록 강도행렬을 제안한다. 변위장은1차 전단변형을 고려한 보 이론을 사용하여 정의되었다. 축방향 변위는 Timoshenko 보이론과 수정된 Vlasov 박벽보 이론을 결합하여 투영단면의 면 변형과 면외 변형의 합으로 나타낸다. 유도된 강성행렬은 휨 전단변형과 뒴 비틂에 의한 영향을 고려한다. 본 유한요소 에서는 2절점, 3절점, 4절점의 세 가지 보요소를 제안하였다. 3절점과 4절점 보 요소는 적층복합 보의 휨 해석에 효과적이었다. 다른 연구자의 수치해석 결과와 비교 검토를 통하여 새로운 유한요소의 활용성과 정확성을 입증하였다.

• Advances in nano research
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• 제8권4호
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• pp.293-305
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• 2020

In the current research, the free vibrational behavior of the FG nano-beams integrated in the hygro-thermal environment and reposed on the elastic foundation is investigated using a novel integral Timoshenko beam theory (ITBT). The current model has only three variables unknown and requires the introduction of the shear correction factor because her uniformed variation of the shear stress through the thickness. The effective properties of the nano-beam vary according to power-law and symmetric sigmoid distributions. Three models of the hygro-thermal loading are employed. The effect of the small scale effect is considered by using the nonlocal theory of Eringen. The equations of motion of the present model are determined and resolved via Hamilton principle and Navier method, respectively. Several numerical results are presented thereafter to illustrate the accuracy and efficiency of the actual integral Timoshenko beam theory. The effects of the various parameters influencing the vibrational responses of the P-FG and SS-FG nano-beam are also examined and discussed in detail.

• 한국기계가공학회지
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• 제19권7호
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• pp.35-40
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• 2020

This work is concerned with various planar deformations of an isotropic sandwich beam, which generally consists of three layers: two stiff skin layers and one soft core layer. When one layer of the sandwich beam is modeled as a beam, the variational-asymptotic method is rigorously used to construct a zeroth-order beam model, which is similar to a generalized Timoshenko beam model capable of capturing the transverse shear deformations but still carries out the zeroth-order approximation. To analyze the planar sandwich beam, the sum of the energies of the two skin layers and one core layer is then formulated with different material and geometric properties and represented by a universal beam model in terms of the core-layer kinematics through interface displacement and stress continuity conditions. As a preliminary validation, two extreme examples are presented to demonstrate the capability and accuracy of this present approach.