• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.689-694
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• 2000

This paper presents a modeling method for the vibration analysis of cantilever beams with an elastically restrained root. Mass and stiffness matrices are derived explicitly by considering the elastically restrained root coupling effect between stretching and bending motion. Numerical results show that the two effects influence the vibration characteristics of rotating beams significantly. The results also present the magnitude of the elastic stiffness of the root to avoid the dynamic buckling. The method presented in this paper can be used to provide accurate predictions of the variations of natural frequencies of rotating beams with an elastically restrained root.

• Structural Engineering and Mechanics
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• v.16 no.2
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• pp.195-217
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• 2003

This paper, which is an extension of a previous work by Viola et al. (2002), deals with the dynamic stability of beams under a triangularly distributed sub-tangential forces when the effect of an elastically restrained end is taken into account. The sub-tangential forces can be realised by a combination of axial and tangential follower forces, that are conservative and non-conservative forces, respectively. The studied beams become unstable in the form of either flutter or divergence, depending on the degree of non-conservativeness of the distributed sub-tangential forces and the stiffness of the elastically restrained end. A non-conservative parameter ${\alpha}$ is introduced to provide all possible combinations of these forces. Problems of this kind are usually, at least in the first approximation, reduced to the analysis of beams according to the Bernoulli-Euler theory if shear deformability and rotational inertia are negligible. The equation governing the system may be derived from the extended form of Hamilton's principle. The stability maps will be obtained from the eigenvalue analysis in order to define the divergence and flutter domain. The passage from divergence to flutter is associated with a noticeable lowering of the critical load. A number of particular cases can be immediately recovered.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.10
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• pp.140-147
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• 1998

The dynamic behavior of elastically restrained beams under the action of distributed tangential forces is investigated in this paper. The beam, which is fixed at one end, is assumed to rest on an intermediate spring support. The governing equations of motion are derived from the energy expressions, and the finite element formulation is employed to calculate the critical distributed tangential force. Jump phenomena for the critical distributed tangential force and instability types are presented for various spring stiffnesses and support positions. Stability maps are generated by performing parametric studies to show how the distributed tangential forces affect the frequencies and the stability of the system considered. Through the numerical simulations, the following conclusioils are obtained: (i) Only flutter type instability exists for the dimensionless spring stiffness K $\leq$ 97, regardless of the position of the spring support. (ii) For the dimensionless spring stiffness K $\leq$ 98, the transition from flutter to divergence occurs at a certain position of the spring support, and the transition position moves from the free end to the free end of the beam as the spring stiffness increases. (iii) For K $\leq$ 10$^{6}$ the support condition can be regarded as a rigid support condition.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.275-280
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• 2003

This paper discusses on the dynamic responsed of an elastically restrained beam under a moving mass of constant velocity. Governing equations of motion taking into account of all inertia effects of the moving mass were derived by Galerkin's mode summation method, and Runge-Kutta integration method was applied to solve the differential equations. Numerical solutions for dynamic deflections of beams were obtained for the changes of the various parameters (spring stiffness, spring position, mass ratios and velocity ratios of the moving mass). In order to verify the numerical predictions for the dynamic response of the beam, experiments were conducted. Numerical solutions for the dynamic responses of the test beam have a good agreement with experimental ones.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1995.04a
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• pp.116-120
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• 1995

본 연구의 목적은 탄성 스프링 지지된 외팔보 모델의 고유진동수를 엄밀해, 유한요소법의 근사해, 실험 값을 비교하여 해의 타당성을 검토하고, 진동 특성을 분석함으로서 이러한 보 모델에 대한 유용한 설계 기초자료를 얻는데 있다.

• Smart Structures and Systems
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• v.30 no.2
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• pp.173-181
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• 2022

The current paper presents a technique to detect crack in non-uniform cantilever-type pipe beams, that have step changes in the properties of their cross sections, restrained by a translational and rotational spring with a tip mass at the free end. An equation for estimating the natural frequencies for the non-uniform beams is derived using the boundary and continuity conditions, and an equivalent bending stiffness for cracked beam is applied to calculate the natural frequencies of the cracked beam. An experimental study for a step-changed non-uniform cantilever-type pipe beam restrained by bolts with a tip mass is carried out to verify the proposed method. The translational and rotational spring constants are updated using the neural network technique to the results of the experiment for intact case in order to establish a baseline model for the subsequent crack detection. Then, several numerical simulations for the specimen are carried out using the derived equation for estimating the natural frequencies of the cracked beam to construct a set of training patterns of a neural network. The crack locations and sizes are identified using the trained neural network for the 5 damage cases. It is found that the crack locations and sizes are reasonably well estimated from a practical point of view. And it is considered that the usefulness of the proposed method for structural health monitoring of the step-changed non-uniform cantilever-type pipe beam-like structures elastically restrained in the ground and have a tip mass at the free end could be verified.

• Smart Structures and Systems
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• v.21 no.3
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• pp.349-358
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• 2018

This paper investigates the free vibration analysis of double-beam system coupled by a two-degree-of-freedom mass-spring system. In order to generalize the model, the main beams are assumed to be elastically restrained against translation and rotation at one end and free at the other. Furthermore, the mass-spring system is elastically connected to the beams at adjustable positions by means of four translational and rotational springs. The governing differential equations of the beams and the mass-spring system are derived and analytically solved by using the Fourier transform method. Moreover, as a second way, a finite element solution is derived. The frequency parameters and mode shapes of some diverse cases are obtained using both methods. Comparison of obtained results by two methods shows the accuracy of both solutions. The influence of system parameters on the free vibration response of the studied mechanical system is examined.

• Journal of KSNVE
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• v.10 no.6
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• pp.1022-1028
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• 2000

This paper presents a modeling method for the vibration analysis of rotating cantilever beams considering the elastic foundation effect. Mass and stiffness matrices are derided explicitly by considering coupling effect between stretching and bonding motion. Numerical results show that the bending direction elastic foundation stiffness influences the vibration characteristics significantly in practical range of beam configuration. The ranges of elastic foundation stiffness to avoid the dynamic buckling are also presented. The method presented in this paper can be used to predict the variations of natural frequencies of rotating cantilever beams with elastically restrained root.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.11
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• pp.317-325
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• 2020

The development of a technique that can monitor the cracks, which is one of the typical types of damage, is necessary to secure the structural safety of elastically restrained cantilever-type beams with a tip mass that is used widely in infrastructure. Impedance techniques have been actively researched to detect cracks, and the cracks were estimated mainly by experimentally investigating the relationship between the crack and impedance signal. This study examined the correlation between the change in the impedance signals due to the crack, and the natural frequency obtained analytically. After updating the analysis model for the intact beam, the impedance signal was measured while gradually inflicting cracks in the cantilever-type beam, and the damage index was obtained. The results were compared with the natural frequencies calculated from the updated analysis model to investigate the correlation. A close correlation was observed between the experimentally obtained impedance damage index, and the analytically calculated natural frequency. Using this correlation, the structural characteristics could be evaluated more accurately from the damage estimation results, and the behavior of the structure could be predicted effectively using the analysis model.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.6
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• pp.1496-1502
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• 1994

The influences of spring position and spring stiffness on the critical force of a cantilevered beam subjected to a follower force are investigated. The spring attatched to the beam is assumed to be a translational one and can be located at arbitrary positions of the beam as it has not been assumed so far. The effects of transeverse shear deformation and rotary intertia of the beam are also included in this analysis. The charateristic equation for the system is derived and a finite element model of the beam using local coordinates is formulated through extended Hamilton's principle. It is found that when the spring is located at position less than that of 0.5L, the flutter type instability only exists. It is shown that the spring position approaches to the free end of the beam from its midpoint, instability type is changed from flutter to divergence through the jump phenomina according to the increase of spring stiffness.