• Transactions of the Korean Society of Mechanical Engineers
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• v.8 no.2
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• pp.119-126
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• 1984

An analysis is presented for the vibration and stability of Beck's column carring a tip mass at its free and subjected there to a follower compressive force by using variational approach. The influence of transverse shear deformation and rotatory inertial of the mass of the column upon the critical flutter load and frequency is considered, and Timoshenko's shear coefficient K' is calculated by Cowper's formulae. It is, moreover, worth noticing that the influence of inertial moment of tip mass upon the flutter load and frequency is investigated. The centroid of a tip mass is offset from the free end of the beam and located along its extended axis of the two cases, one of which has a tip mass increasing as .xi., the tip mass offset parameter, is augmented, the other has a tip mass constant but the inertial moment is variable according to a magnitude of .eta., the tip mass offset parament. This study reveals that the effects of inertial moment of a tip mass and larger value of P are specially remarkable even a tip mass is a same.

• Structural Engineering and Mechanics
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• v.45 no.1
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• pp.69-93
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• 2013

The present study deals with the dynamics of the flapwise (out-of-plane) vibrations of a rotating, internally damped (Kelvin-Voigt model) tapered Bernoulli-Euler beam carrying a heavy tip mass. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The equation of motion and the corresponding boundary conditions are derived via the Hamilton's Principle, leading to a differential eigenvalue problem. Afterwards, this eigenvalue problem is solved by using Frobenius Method of solution in power series. The resulting characteristic equation is then solved numerically. The numerical results are tabulated for a variety of nondimensional rotational speed, tip mass, tip mass offset, mass moment of inertia, internal damping parameter, hub radius and taper ratio. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.4 s.97
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• pp.483-491
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• 2005

In this paper a dynamic behavior of a double-cracked cantilever pipe with the tip mass and a moving mass is presented. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by using Lagrange's equation. The influences of the moving mass, the tip mass and double cracks have been studied on the dynamic behavior of a cantilever pipe system by numerical method. The cracks section are represented by the local flexibility matrix connecting two undamaged beam segments. Therefore, the cracks are modelled as a rotational spring. This matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. We investigated about the effect of the two cracks and a tip mass on the dynamic behavior of a cantilever pipe with a moving mass.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.713-716
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• 2004

In this paper a dynamic behavior of a double-cracked cnatilver beam with a tip mass and the moving mass is presented. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by using Lagrange's equation. The influences of the moving mass, a tip mass and double cracks have been studied on the dynamic behavior of a cantilever beam system by numerical method. The cracks section are represented by the local flexibility matrix connecting two undamaged beam segments. ,Therefore, the cracks are modelled as a rotational spring. Totally, as a tip mass is increased, the natural frequency of cantilever beam is decreased. The position of the crack is located in front of the cantilever beam, the frequencies of a double-cracked cantilever beam presents minimum frequency.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.04a
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• pp.309-315
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• 1996

An analysis is presented on the stability of elastic cantilever column subjected to uniformly distributed follower forces as to the influence of the elastic restraints and a tip mass at the free end. The elastic restraints are formed by both the translational and the rotatory springs. For this purpose, the governing equations and boundary conditions are derived by using Hamilton's principle, and the critical flutter loads and frequencies are obtained from the numerical evaluation of the eigenvalue functions of this elastic system. The added tip mass increases as a whole the critical flutter load in this system, but the presence of its moment of inertia of mass has a destabilizing effect. The existence of the translational and rotatory spring at the free end increases the critical flutter load of the elastic cantilever column. Nevertheless their effects on the critical flutter load are not uniform because of their coupling. The translational spring restraining the end of cantilever column decreases the critical flutter load by coupling with a large value of tip mass, while by coupling with the moment of inertia of tip mass its effect on the critical flutter load is contrary. The rotatory spring restraining the free end of cantilever column increases the critical flutter load by coupling with the tip mass, but decreases it by coupling with the moment of inertia of tip mass.

• Journal of Mechanical Science and Technology
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• v.19 no.9
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• pp.1731-1741
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• 2005

In this paper, we studied about the effect of the open crack and a tip mass on the dynamic behavior of a cantilever pipe conveying fluid with a moving mass. The equation of motion is derived by using Lagrange's equation and analyzed by numerical method. The cantilever pipe is modelled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influences of the crack, the moving mass, the tip mass and its moment of inertia, the velocity of fluid, and the coupling of these factors on the vibration mode, the frequency, and the tip-displacement of the cantilever pipe are analytically clarified.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.1036-1041
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• 1993

The tip of the flexible robot arm has to be controlled by the active control reducing vibration because it has residual vibration after getting to desired position. This paper presents an end-point position control of a 1-link flexible robot arm having tip mass by the PID control algorithm. The system is composed of a flexible arm with tip mass, dc servomotor and ballscrew mechanism under translational motion. The feedback signal composed of the tip displacement measured by laser sensor, estimated velocity and acceleration is used to control the base motion. Theoretical results are obtained by applying the Laplace transform and the numerical inversion method to the governing equations. After the flexible robot arm reaches to. the desired position, the residual vibration is controlled by the PID algorithm. This paper gives the simulation and experimental results of end-point responses according to changing tip-mass and arm length. And this algorithm shows good effects of reducing the residual vibration. Approximately, theoretical response is in good agreement with experimental one.

• Journal of KSNVE
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• v.7 no.1
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• pp.91-97
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• 1997

An analysis is presented on the stability of an elastic cantilever column having the elastic restraints at its free end, carrying an added tip mass, and subjected to uniformly distributed follower forces. The elastic restraints are formed by both a translational spring and a rotatory spring. For this purpose, the governing equations and boundary conditions are derived by using Hamilton's principle, and the critical flutter loads and frequencies are obtained from the numerical evaluation of the eigenvalue functions of this elastic system. The added tip mass increases as a whole the critical flutter load of the elastic cantilever column, but the presence of its moment of inertia of mass has a destabilizing effect. The existence of the translational and rotatory springs at the free end increases the critical flutter load of the elastic cantilever column. Nevertheless, their effects on the critical flutter load are not uniform because of their coupling. The translational spring restraining the free end of the cantilever column decreases the critical flutter load by coupling with a large value of tip mass, while by coupling with the moment of inertia of tip pass its effect on the critical flutter load is contrary. The rotatory spring restraining the free end of the cantilever column increases the critical flutter load by coupling with the tip mass, but decreases it by coupling with the moment of inertia of the tip mass.

• Journal of the Korean Society of Safety
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• v.13 no.4
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• pp.49-58
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• 1998

On the stability of the Timoshenko cantilever column subjected of a compressive follower force, the influences of the moment of inertia of the tip mass at the free end and the characteristics of a translational spring at the free end of the column are studied. The equations of motion and boundary conditions of system are estabilished by using the d'Alembert virtual work of principle. On the evaluation of stability of the column, the effect of the shear deformation and rotatory inertia is considered in calculation. The moment of inertia of the tip mass at the free end of the column is changed by adjusting the distance c, from the free end of the column to the tip mass center. The free end of the column is supported elastically by a translational spring. For the maintenance of the good stability of the column, it is also proved that the constant of the translational spring at the free end must be very large for the case without a tip mass while it must be small for the case with a tip mass. Therefore, it is found that the shape of the tip mass and the characteristic of the spring at the free end are very effective elements for the stability of the column when the columns subjected to a compressive follower force are designed.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.10
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• pp.976-982
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• 2007

In this paper the vibration system is consisted of a rotating cantilever pipe conveying fluid and tip mass. The equation of motion is derived by using the Lagrange's equation. The system of pipe conveying fluid becomes unstable by flutter. Therefore, the influence of a rotating angular velocity, mass ratio, the velocity of fluid flow and tip mass on the stability of a cantilever pipe by the numerical method are studied. The critical flow velocity for flutter is proportional to the angular velocity and tip mass of the cantilever pipe. Also, the critical flow velocity and stability maps of the pipe system are obtained by changing the mass ratios.