• International Journal of Precision Engineering and Manufacturing
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• v.2 no.4
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• pp.30-39
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• 2001

This paper investigates vibrational motion of a flexible beam fixed on a moving cart and carrying a moving mass. The equations of motion of the beam-mass-cart system are analysed through the unconstrained modal analysis. The exact normal mode solution used in modal analysis correspond to the eigenfrequencies for each position of the moving mass and to the ratios of the weight of the beam-mass-car system. Time solutions of normal modes are also transformed properly according to the position of the moving mass. Numerical simulations are carried out to obtain open-loop responses of the system in tracking pre-designed paths of the moving mass. The simulation results show that the model predicts the dynamic behavior of the beam-mass-cart system well. Experiments are carried out to show the validity of the proposed analytical method.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.11
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• pp.204-212
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• 1999

In this paper, the vibrational motion of a flexible beam clamped on a translating base and carrying a moving mass is investigated. The equations of motion which describe the total dynamics of the beam-mass-cart system are derived and the coupled dynamic equations are solved by unconstrained modal analysis. In modal analysis, the exact normal mode solutions corresponding to the eigenfrequencies for the position of the moving mass and the ratios of the mass of the flexible beam, the moving mass and the base cart are used. Proper transformations of the time solutions between the normal modes for a position and those for the next position of the moving mass are also adopted. Numerical simulations are carried out to obtain the open-loop responses of the system in tracking the pre-designed path of the moving mass.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.401.2-401
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• 2002

An unconstrained tuning fork with a 3-D model has been numerically analyzed by Finite Element Method (FEM) and Boundary Element Method (BEM). The first three natural frequencies were calculated by the FEM modal analysis. Then the change of the modal frequencies was examined with the variation of the tuning fork length and width. (omitted)

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.367-372
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• 1998

In this paper, the mathematical model of a cut with an inverted flexible beam and a concentrated tip mass was derived. The characteristic equation for calculating the natural frequencies of the cart-beam-mass system was obtained and the motion of the system was analyzed through unconstrained modal analysis. A good positioning response of the cart without excessive vibrational motion of the tip mass could be obtained through numerical simulation using PID controller with the feedback of both the position of the cart and the deflection of the beam.

• The Journal of the Acoustical Society of Korea
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• v.21 no.3E
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• pp.112-118
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• 2002

An unconstrained tuning fork with a 3-D model has been numerically analyzed by Finite Element Method (FEM) and Boundary Element Method (BEM). The first three natural frequencies were calculated by the FEM modal analysis. Then the trend of the change of the modal frequencies was examined with the variation of the tuning fork length and width. An formula for the natural frequencies-tuning fork length relationship were derived from the numerical analysis results. Finally the BEM was used for the sound pressure field calculation from the structural displacement data.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.11 s.170
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• pp.1940-1951
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• 1999

In this paper, the equations of motion of a Bernoulli-Euler cantilever beam fixed on a moving cart and carrying a lumped mass concentrated at an arbitrary position along the beam is derived. The motion of the beam-mass-cart system is analyzed through unconstrained modal analysis, and a unified characteristic equation for calculating the natural frequencies of the system is obtained. The changes of natural frequencies and the corresponding mode shapes with respect to the changes in mass ratios of the system and to the concentrated position of the lumped mass are investigated with the frequency equation, which can be generally applied to this kind of systems. The exact and assumed-mode solutions including the dynamics of the base cart are obtained, and the open-loop responses of the system by arbitrarily designed forcing function are given by numerical simulations. The results match well with physical phenomena even at the extreme cases where the concentrated mass is attached to the bottom and to the top of the beam.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.1201-1204
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• 2003

An unconstrained tuning fork with a 3-D model has been numerically analyzed by Finite Element Method(FEM) and Boundary Element Method (BEM). The first three natural frequencies were calculated by the FEM modal analysis. Then the trend of the change of the modal frequencies was examined with the variation of the tuning fork length and width. An formula for the natural frequencies-tuning fork length relationship were derived from the numerical analysis results. Finally the BEM was used fur the sound pressure field calculation from the structural displacement data.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.1049-1053
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• 2002

An unconstrained tuning fork with a 3-D model has been numerically analyzed by Finite Element Method (FEM) and Boundary Element Method (BEM). The first three natural frequencies were calculated by the FEM modal analysis. Then the change of the modal frequencies was examined with the variation of the tuning fork length and width. Analytical model equations were derived from the numerically relating results of the modal frequency-tuning fork length by approximating minimization. Finally the BEM was used for the sound pressure field calculation from the structural displacement data.

• Proceedings of the Acoustical Society of Korea Conference
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• spring
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• pp.465-468
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• 2002

An unconstrained tuning fork with a 3-D model has been numerically analyzed by Finite Element Method (FEM) and Boundary Element Method (BEM). The first three natural frequencies were calculated by the FEM modal analysis. Then the change of the modal frequencies was examined with the variation of the tuning fork length and width. Analytical model equations were derived from the numerically relating results of the modal frequency-tuning fork length by approximating minimization. Finally the BEM was used for the sound pressure field calculation from the structural displacement data.