• Journal of the Korean Society for Precision Engineering
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• v.25 no.6
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• pp.99-107
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• 2008

In this paper, the stability of a cracked cantilever Timoshenko beam with a tip mass subjected to follower force is investigated. In addition, an analysis of the flutter instability(flutter critical follower force) and a critical natural frequency of a cracked cantilever Euler / Timoshenko beam with a tip mass subjected to a follower force is presented. The vibration analysis on such cracked beam is conducted to identify the critical follower force for flutter instability based on the variation of the first two resonant frequencies of the beam. Therefore, the effect of the crack's intensity, location and a tip mass on the flutter follower force is studied. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.3
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• pp.210-216
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• 2003

A nonlinear dynamic modeling method for cantilever beams undergoing axially oscillating motion is presented in this paper. Hybrid deformation variables are employed for the modeling method with which frequency response characteristics of axially oscillating cantilever beams are investigated. It is shown that the geometric nonlinear effects of stretching and curvature play important roles to accurately predict the frequency response characteristics. The effects of the amplitude and the damping constant on the frequency characteristics are also exhibited.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.12
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• pp.1295-1303
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• 2004

In this Paper a dynamic behavior of a cracked cantilever pipe conveying fluid with the moving mass is presented. It has the results focused on the response characteristics. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The cracked section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. When the fluid velocity is constant, the influences of the crack severity, the position of the crack, the moving mass and its velocity, and the coupling of these factors on the tip-displacement of the cantilever pipe are depicted.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.262-267
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• 2002

A nonlinear dynamic modeling method for cantilever beams undergoing axially oscillating motion is presented in this paper. Hybrid deformation variables are employed for the modeling method with which frequency response characteristics of a axially oscillating cantilever beams are investigated. It is shown that the geometric nonlinear effects of stretching and curvature play important roles to accurately predict the frequency response characteristics. The effects of the amplitude and the damping constant on the frequency characteristics are also exhibited.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.12
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• pp.1304-1313
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• 2004

In this paper a dynamic behavior of a cracked cantilever pipe conveying fluid with the moving mass is presented. It has the results focused on the frequency change. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. When the velocity of the moving mass is constant, the influences of the crack severity, the position of the crack, the moving mass, and the coupling of these factors on the frequencies of the cantilever pipe are depicted.

• 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.

• Structural Engineering and Mechanics
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• v.46 no.1
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• pp.39-51
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• 2013

An extremum method is presented to predict the wrinkling characteristics of the inflated cone in bending. The wrinkling factor is firstly defined so as to obtain the wrinkling condition. The initial wrinkling location is then determined by searching the maximum of the wrinkling factor. The critical wrinkling load is finally obtained by determining the ratio of the wrinkling moment versus the initial wrinkling location. The extremum method is proposed based on the assumption of membrane material of beam wall, and it is extended to consider beam wall with thin-shell material in the end. The nondimensional analyses show that the initial wrinkling location is closely related to the taper ratio. When the taper ratio is higher than the critical value, the initial wrinkles will be initiated at a different location. The nondimensional critical wrinkling load nonlinearly increases as the taper ratio increases firstly, and then linearly increases after the critical taper ratio. The critical taper ratio reflects the highest load-carrying efficiency of the inflated cone in bending, and it can be regarded as a measure to optimize the geometry of the inflated cone. The comparative analysis shows fairly good agreement between analytical and numerical results. Over the whole range of the comparison, the mean differences are lower than 3%. This gives confidence to use extremum method for bending-wrinkling analysis of inflated conical cantilever beam.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.3
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• pp.281-289
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• 2016

In this paper, a new dynamic model for modal analysis of a rotating cantilever beam with a tip-mass is developed. The nonlinear strain such as von Karman type and the corresponding linearized stress are used to consider the geometric nonlinearity, and Euler-Bernoulli beam theory is applied in the present model. The nonlinear equations of motion and the associated boundary conditions which include the inertia of the tip-mass are derived through Hamilton's principle. In order to investigate modal characteristics of the present model, the linearized equations of motion in the neighborhood of the equilibrium position are obtained by using perturbation technique to the nonlinear equations. Since the effect of the tip-mass is considered to the boundary condition of the flexible beam, weak forms are used to discretize the linearized equations. Compared with equations related to stiffening effect due to centrifugal force of the present and the previous model, the present model predicts the dynamic characteristic more precisely than the another model. As a result, the difference of natural frequencies loci between two models become larger as the rotating speed increases. In addition, we observed that the mode veering phenomenon occurs at the certain rotating speed.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.11
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• pp.29-34
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• 2020

In this study, a sensitivity formulation was applied to analyze the dynamic response due to the effect of the excitation force for the undamped vibration of the cantilever beam. The theoretically fundamental formulations were derived considering an eigenvalue problem and its modal analysis to govern the second order algebraic differential equation in terms of the change in the modal coordinate with respect to the design parameters. A representative physical quantity pertaining to the dynamic response, that is, the rate of change in the dynamic displacement, was observed by changing the design variables, such as the cross-sectional area of the beam. The numerical results were obtained at various locations, considering the application of the external forces and observation of the dynamic displacement. When the detection position was closer to the free end of the cantilever beam, the sensitivity of the dynamic displacement was higher, as predicted through the oscillating motion of the beam. The presented findings can provide guidance to compute the dynamic sensitivity for a flexibly connected structure under dynamic excitations.

• 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.