• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.1
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• pp.11-21
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• 2004

In this paper, an active vibration control of a tensioned elastic axially moving string is investigated. The dynamics of the translating string ale described by a non-linear partial differential equation coupled with an ordinary differential equation. The time varying control in the form of the right boundary transverse motions is suggested to stabilize the transverse vibration of the translating continuum. A control law based on Lyapunov's second method is derived. Exponential stability of the translating string under boundary control is verified. The effectiveness of the proposed controller is shown through the simulations.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2260-2265
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• 2005

In this paper, an active vibration control of a tensioned elastic axially moving string is investigated. The dynamics of the translating string are described by a non-linear partial differential equation coupled with an ordinary differential equation. A time varying control in the form of right boundary transverse motions is proposed in stabilizing the transverse vibrations of the translating continuum. A control law based on Lyapunov's second method is derived. Exponential stability of the closed-loop system is verified. The effectiveness of the proposed controller is shown through simulations.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2474-2479
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• 2005

The control objectives in this paper are to move the gantry of a container crane to its target position and to suppress the transverse vibration of the payload. The crane system is modeled as an axially moving nonlinear string equation, in which control inputs are applied at both ends, through the gantry and the payload. The dynamics of the moving string are derived using Hamilton's principle. The Lyapunov function method is used in deriving a boundary control law, in which the Lyapunov function candidate is introduced from the total mechanical energy of the system. The performance of the proposed control law is compared with other two control algorithms available in the literature. Experimental results are given.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.387-392
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• 2004

The control objectives in this paper are to move the gantry of a container crane to its target position and to suppress the transverse vibration of the payload. The crane system is modeled as an axially moving string equation, in which control inputs are applied at both ends, through the gantry and the payload. The dynamics of the moving string are derived using Hamilton's principle for systems with changing mass. The Lyapunov function method is used in deriving a boundary control law, in which the Lyapunov function candidate is introduced from the total mechanical energy of the system. The performance of the proposed control law is compared with other two control algorithms available in the literature. Experimental results are given.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.7
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• pp.98-105
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• 2020

This study deals with the passive control of the dynamic characteristics of a theoretical model which is a string with fixed ends and loaded by two point masses - a main mass (M_o) and a secondary mass (M_s). It has been controlled passively by means of a relocation of a secondary mass. A main mass placed on the string is considered as a vibrating receiver which be forced to vibrate by a vibrating source being positioned on the string. By analyzing the motion of a string, the equation of motion for a string was derived by using a method of variation of parameters. To define the optimal conditions for the vibration reduction, the governing equation, which denotes the dynamic response of a string was derived in the closed form and then evaluated numerically. The possibility of reduction of an amplitude and a power being transmitted to a main mass were found to depend on the location and the magnitude of a secondary mass as well as the range of a forcing frequency.

• International Journal of Control, Automation, and Systems
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• v.3 no.4
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• pp.601-611
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• 2005

In this paper, an active vibration control of a tensioned, elastic, axially moving string is investigated. The dynamics of the translating string are described with a non-linear partial differential equation coupled with an ordinary differential equation. A right boundary control to suppress the transverse vibrations of the translating continuum is proposed. The control law is derived via the Lyapunov second method. The exponential stability of the closed-loop system is verified. The effectiveness of the proposed control law is simulated.

• The Journal of the Acoustical Society of Korea
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• v.38 no.6
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• pp.710-715
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• 2019

A transmission line based bowed string model is built by analogizing a vibrating string to an electrical transmission line and implementing the calculation for the frictional bow-string force given by a digital bow into a circuit. The performance of the proposed model is demonstrated by showing that the velocity of the string at the bowing point from the proposed model is consistent with that from the finite difference form of the wave equation for a bowed string by the digital bow.

• The Journal of the Acoustical Society of Korea
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• v.20 no.1
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• pp.3-12
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• 2001

In physical modeling of plucked string instruments, the vibration of a string is typically simulated by the linear system. Currently the Digital Waveguides of J.O.Smith[1] are widely used to get a high quality sound of the plucked string instrument. He used the wave equation to derive the Digital Waveguides and emphasized the time variable. In this thesis, new model of plucked string is proposed to improve the sound quality emphasizing the spatial variable of the wave equation. In our model, we used the fixed sampling interval which is not dependent on the speed of the wave. So we could get more detailed description of wave movement by the time variable. As a result, the new model could produce a higher quality sound of plucked string instrument.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.731-736
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• 2000

The vibration of an axially moving string is studied when the string has geometric non-linearity and translating acceleration. Based upon the von karman strain theory, The equation for the longitudinal vibration is linear and uncoupled, while the equation for the transverse vibration is non-linear and coupled between the longitudinal and transverse deflections. The governing equations are discretized by using the Galerkin approximation. With the discretized nonlinear equations, the time responses are investigated by using the generalized-${\alpha}$ method.

• Journal of KSNVE
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• v.10 no.5
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• pp.838-842
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• 2000

The vibration of an axially moving string is studied when the string has geometric non-linearity and translating acceleration. Based upon the von karman strain theory, the equations of motion are derived considering the longitudinal and transverse deflection. The equation for the longitudinal vibration is linear and uncoupled, while the equation for the transverse vibration is non-linear and coupled between the longitudinal and transverse deflections. These equations are discretized by using the Galerkin approximation after they are transformed into the variational equations, i.e. the weak forms so that the admissible and comparison functions can be used for the bases of the longitudinal and transverse deflections respectively. With the discretized nonlinear equations, the time responses are investigated by using the generalized-$\alpha$ method.