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.

Active Wave Cancellation of the Axially Moving String

2001 ◽  
Author(s):  
Chin An Tan ◽  
Shenger Ying
Keyword(s):  
Boundary Conditions ◽  
Initial Conditions ◽  
General Boundary ◽  
Closed Form Expression ◽  
Control Law ◽  
General Boundary Conditions ◽  
Axially Moving String ◽  
Axially Moving ◽  
Active Wave ◽  
Control Forces

Abstract The active wave control of the linear, axially moving string with general boundary conditions is presented in this paper. Considerations of general boundary conditions are important from both practical and experimental viewpoints. The active control law is established by employing the idea of wave cancellation. An exact, closed-form expression for the transverse response of the controlled system, consisting of the flexible structure, the wave controller, and the sensing and actuation devices, is derived in the frequency domain. Two actuation forces, one upstream and one downstream of an excitation force, are applied. The proposed control law shows that all modes of the string are controlled and the vibration in the regions upstream and downstream of the control forces can be cancelled. However, these results are based on ideal conditions and the assumption of zero initial conditions at the non-fixed boundaries. Effects of non-zero boundary motions at the instant of application of the control forces are examined and the control is shown to be effective under these conditions. The stability and robustness of the control forces are improved by the introduction of a stabilization coefficient in the control law. The effectiveness, robustness and stability of the control forces are demonstrated by simulations and verified by experiments on axially moving belt drive and chain drive systems.

Dynamic Analysis of the Axially Moving String Based on Wave Propagation

1995 ◽  
Author(s):  
S. Ying ◽  
C. A. Tan
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Time Domain ◽  
General Boundary Conditions ◽  
Axially Moving String ◽  
Convolution Integrals ◽  
Axially Moving ◽  
The Time Domain ◽  
Transverse Response ◽  
Physical Boundary

Abstract This paper presents an exact solution for the transverse response of an axially moving string under general boundary conditions. The response solution is derived in the frequency domain and interpreted in terms of wave propagation functions. The response in the time domain involves only several convolution integrals which can easily be obtained for many physical boundary conditions. The transient response of the translating string with a spring or a dashpot at a boundary is presented.

scholarly journals Vibration of Roller Chain Drives at Low, Medium and High Operating Speeds

1993 ◽  
Author(s):  
Woosuk Choi ◽  
Glen E. Johnson
Keyword(s):  
Boundary Conditions ◽  
Transverse Vibration ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Partial Differential ◽  
Periodic Load ◽  
Roller Chain ◽  
Axially Moving ◽  
The Impact ◽  
Chain Drives

Abstract A model based on axially moving material is developed to study transverse vibration in roller chain drives. A unique feature of the work presented in this study is that impact, polygonal action and external periodic load have been included through chain tension and boundary conditions and periodic length change is also considered. The impact between the engaging roller and sprocket surface is modeled as a single impact between two elastic bodies and the modeling of the polygonal action is based on a four bar mechanism (rigid four bar at low speeds, elastic four bar at moderate and high speeds). At low and medium operating speeds, the system equation of motion for the chain span is expressed as a mixed type partial differential equation with time-dependent coefficients and time-dependent boundary conditions. At high operating speeds, the system equations of motion are two partial differential equations for transverse and longitudinal vibrations respectively and they are nonlinearly coupled The effects on transverse vibration of center distance, the moment of inertia of the driven sprocket system, static tension, and external periodic load are presented and discussed. Solutions are obtained by a finite difference method and Galerkin’s method.

Dynamic Analysis of the Axially Moving String Based on Wave Propagation

1997 ◽  
Vol 64 (2) ◽  
pp. 394-400 ◽  
Author(s):  
C. A. Tan ◽  
S. Ying
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Computation Time ◽  
Propagation Speed ◽  
Axially Moving String ◽  
Convolution Integrals ◽  
Axially Moving ◽  
The Time Domain ◽  
Transverse Response ◽  
Physical Boundary

In this paper, we present an exact solution for the linear, transverse response of an axially moving string with general boundary conditions. The solution is derived in the frequency domain and interpreted in terms of wave propagation functions. The boundary effects are included by the use of compliance functions at the boundaries. The response in the time domain involves only several convolution integrals which can easily be obtained for many physical boundary conditions. A comparison of this method with an existing solution method shows that this method requires much less computation time. The transient response of the translating string with a spring or a dashpot at a boundary is presented. It is shown that complete wave absorption occurs at a boundary when that boundary has a dashpot with damping coefficient equal to the propagation speed of the reflected wave.

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.

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