Linear transverse vibration of an axially moving string–particle system

1988 ◽  
Vol 84 (3) ◽  
pp. 963-969 ◽  
Author(s):  
J. A. Wickert ◽  
C. D. Mote
Keyword(s):  
Transverse Vibration ◽  
Particle System ◽  
Axially Moving String ◽  
Axially Moving

Reduction of Vibration for an Axially Moving String With a Tensioner

2005 ◽  
Author(s):  
Li-Qun Chen ◽  
Wei Zhang
Keyword(s):  
Energy Dissipation ◽  
Boundary Conditions ◽  
Governing Equation ◽  
Transverse Vibration ◽  
Vibration Reduction ◽  
Reflection And Transmission ◽  
Axially Moving String ◽  
Optimal Damping ◽  
Axially Moving ◽  
Nicolson Scheme

This paper deals with reducing transverse vibration for an axially moving string by a damped tensioner. The governing equation and the boundary conditions are derived for the system. Based on the analysis of the reflection and transmission of waves propagating along the string, the maximal energy dissipation is realized by determining the optimal damping. To simulate numerically the effect of vibration reduction, the Crank-Nicolson scheme is applied to discretize the governing equation of the string. The numerical results demonstrate the optimality of the determined damping in suppressing the transverse vibration.

Boundary Control of an Axially Moving String Via Lyapunov Method

1999 ◽  
Vol 121 (1) ◽  
pp. 105-110 ◽  
Author(s):  
Rong-Fong Fung ◽  
Chun-Chang Tseng
Keyword(s):  
Boundary Control ◽  
Lyapunov Method ◽  
Sliding Mode ◽  
Semigroup Theory ◽  
Active Vibration Control ◽  
Nonlinear Partial Differential Equation ◽  
Distributed Parameter ◽  
Axially Moving String ◽  
Active Vibration ◽  
Axially Moving

This paper presents the active vibration control of an axially moving string system through a mass-damper-spring (MDS) controller at its right-hand side (RHS) boundary. A nonlinear partial differential equation (PDE) describes a distributed parameter system (DPS) and directly selected as the object to be controlled. A new boundary control law is designed by sliding mode associated with Lyapunov method. It is shown that the boundary feedback states only include the displacement, velocity, and slope of the string at RHS boundary. Asymptotical stability of the control system is proved by the semigroup theory. Finally, finite difference scheme is used to validate the theoretical results.

Research on the Vibration of Sheet Metal near the Zinc Pot Area in Continuous Hot-Dip Galvanizing Line

2011 ◽  
Vol 141 ◽  
pp. 471-477 ◽  
Author(s):  
Pei Min Xu ◽  
Biao Wang ◽  
Jin Jie Ye ◽  
Hai Juan Zhang ◽  
Zhi Lai Huang ◽  
...  
Keyword(s):  
Sheet Metal ◽  
Transverse Vibration ◽  
Cooling Tower ◽  
The Other ◽  
Control Parameters ◽  
Main Factors ◽  
Axially Moving ◽  
Vibration Tests ◽  
Air Knife ◽  
Excited Resonance

Large vibration of the sheet metal near the air knife is one of the main factors controlling the accuracy of thickness of the cladding zinc in continuous hot-dip galvanizing line. Lots of vibration tests are carried out on the strip and main equipments in the zinc pot area of a galvanizing line during downtime and operation in order to diagnose causes of the large vibration of the strip near the air knife. Theoretic foundation of adjustment of control parameters to suppress the strip vibration is established. Main mechanisms of large vibration of the strip are found by the theory of the transverse vibration of axially moving continua. The first one is the resonance of forced vibration induced by support movement aroused by passive rollers’ sloshing in the zinc pot, and the other is the parametrically excited resonance of the strip induced by tension fluctuation enlarged by local structural resonances of the cooling tower.

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