• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.703-706
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• 1999

In this paper, robust vibration control of a one-link flexible robot arm based on variable structure system is discussed. We derive dynamic equations of it using a Lagragian assumed modes method based on Bernoulli-Euler beam theory. The optimal sliding surface is designed and the problem of chattering is also solved by the adoptation of a continuous control law within a small neighborhood of the switching hyperplane.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.04a
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• pp.679-680
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• 2011

The Forced vibration characteristics of elastically restrained pipe conveying fluid with the attached mass are investigated in this paper. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by using Hamilton's principle. The effect of attached mass and spring constant on forced vibration of pipe system is studied. Also, the critical flow velocities and stability maps of the valve-pipe system are obtained as each parameters.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.435-440
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• 2002

The free vibration of partially embedded piles is investigated. The pile model is based on the Bernoulli-Euler beam theory and the soil is idealized as a Winkler model for mathematical simplicity. The governing differential equation for the free vibrations of such members is solved numerically The piles with one typical end constraint (clamped/hinged/free) and the other hinged end with rotational spring are applied in numerical examples. The lowest three natural frequencies are calculated over a range of non-dimensional system parameters: the rotational spring parameter, the relative stiffness and the embedded ratio.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.11a
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• pp.649-654
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• 2000

The non-linear differential equations of motion of a fluid conveying curved pipe are derived by making use of Hamiltonian approach. The extensible dynamics of the pipe is based on the Euler-Bernoulli beam theory. Some significant differences between linear and nonlinear equations and the basic analysis results are discussed. Using eigenfrequency analysis, it can be shown that the natural frequencies are changed with flow velocity.

• Interaction and multiscale mechanics
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• v.3 no.4
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• pp.321-331
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• 2010

A new technique is proposed for bridge structural damage detection based on spatial wavelet analysis of the time history obtained from vehicle body moving over the bridge, which is different from traditional detection techniques based on the bridge response. A simply-supported Bernoulli-Euler beam subjected to a moving spring-mass unit is established, with the crack in the beam simulated by modeling the cracked section as a rotational spring connecting two undamaged beam segments, and the equations of motion for the system is derived. By using the transfer matrix method, the natural frequencies and mode shapes of the cracked beam are determined. The responses of the beam and the moving spring-mass unit are obtained by modal decomposition theory. The continuous wavelet transform is calculated on the displacement time histories of the sprung-mass. The case study result shows that the damage location can be accurately determined and the method is effective.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.600-603
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• 2005

In this paper we studied about the effect of the double cracks on the dynamic behavior of a simply supported beam. The equation of motion is derived by using Lagrange's equation and analyzed by numerical method. The simply supported beam is modeled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting three undamaged beam segments. The influences of the crack depth and position of each crack on the vibration mode and the natural frequencies of a simply supported beam are analytically clarified. The theoretical results are also validated by a comparison with experimental measurements.

• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.145-153
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• 2017

In this article, a novel simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) beams is proposed. The beauty of this theory relies on its 2-unknowns displacement field as the Euler-Bernoulli beam theory, which is even less than the Timoshenko beam theory. A shear correction factor is, therefore, not needed. Equations of motion are obtained via Hamilton's principle. Analytical solutions for the bending and free vibration analysis are given for simply supported beams. Efficacy of the proposed model is shown through illustrative examples for bending and dynamic of FG beams. The numerical results obtained are compared with those of other higher-order shear deformation beam theory results. The results obtained are found to be accurate.

• Journal of Ocean Engineering and Technology
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• v.17 no.6
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• pp.47-52
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• 2003

To determine the effect of transverse open crack on the dynamic behavior of simply-supported Euler-Bernoulli beam with the moving masses, an iterative modal analysis approach is developed. The influence of depth and position of the crack in the beam, on the dynamic behavior of the simply supported beam system, have been studied by numerical method. The cracked section is represented by a local flexibility matrix, connecting two undamaged beam segments that is, the crack is modeled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section, and is derived by applying a fundamental fracture mechanics theory. As the depth of the crack is increased, the mid-span deflection of the simply-supported beam, with the moving mass, is increased. The crack is positioned in the middle point of the pipe, and the mid-span defection of the simply-supported pipe represents maximum deflection.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1360-1365
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• 2006

In this paper the vibration analysis of cantilever beams having a concentrated tip mass and an open crack are performed. The influences of a concentrated tip mass, the crack depth, and the crack position on the natural frequencies of the cracked cantilever beam are investigated by a numerical method. The cracked cantilever beam is modeled based on the Euler-Bernoulli beam theory. The flexibility due to crack is calculated using a fracture mechanics theory. The crack is assumed to be opened during the vibrations. The results obtained by the present method were compared with experimental results to verify the theory. As inspected, as the crack depth and the concentrated tip mass increase, the natural frequencies of the beam decrease. In general, the natural frequencies of the cantilever beam are more sensitive to the depth of the crack than the position of the crack.

• Steel and Composite Structures
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• v.42 no.1
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• pp.75-90
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• 2022

The pointwise equilibrium polynomial (PEP) element considering local second-order effect has been widely used in direct analysis of many practical engineering structures. However, it was derived according to Euler-Bernoulli beam theory and therefore it cannot consider shear deformation, which may lead to inaccurate prediction for deep beams. In this paper, a novel beam-column element based on Timoshenko beam theory is proposed to overcome the drawback of PEP element. A fifth-order polynomial is adopted for the lateral deflection of the proposed element, while a quadric shear strain field based on equilibrium equation is assumed for transverse shear deformation. Further, an additional quadric function is adopted in this new element to account for member initial geometrical imperfection. In conjunction with a reliable and effective three-dimensional (3D) co-rotational technique, the proposed element can consider both member initial imperfection and transverse shear deformation for second-order direct analysis of frame structures. Some benchmark problems are provided to demonstrate the accuracy and high performance of the proposed element. The significant adverse influence on structural behaviors due to shear deformation and initial imperfection is also discussed.