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.

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.

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.

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.

Influence of the applied pressure of the transducer on the propagation speed of the ultrasonic wave in wood

Holzforschung ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Edgar V.M. Carrasco ◽  
Rejane C. Alves ◽  
Mônica A. Smits ◽  
Vinnicius D. Pizzol ◽  
Ana Lucia C. Oliveira ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Applied Pressure ◽  
Pressure Gauge ◽  
Eucalyptus Grandis ◽  
Propagation Speed ◽  
Ultrasonic Waves ◽  
Ultrasonic Speed ◽  
Wave Propagation Speed ◽  
Propagation Technique ◽  
Non Destructive

Abstract The non-destructive wave propagation technique is used to estimate the wood’s modulus of elasticity. The propagation speed of ultrasonic waves is influenced by some factors, among them: the type of transducer used in the test, the form of coupling and the sensitivity of the transducers. The objective of the study was to evaluate the influence of the contact pressure of the transducers on the ultrasonic speed. Ninety-eight tests were carried out on specimens of the species Eucalyptus grandis, with dimensions of 120 × 120 × 50 mm. The calibration of the pressure exerted by the transducer was controlled by a pressure gauge using a previously calibrated load cell. The robust statistical analysis allowed to validate the experimental results and to obtain consistent conclusions. The results showed that the wave propagation speed is not influenced by the pressure exerted by the transducer.

Optimized Mooring Line Simulation Using a Hybrid Method Time Domain Scheme

2014 ◽  
Author(s):  
Niels Hørbye Christiansen ◽  
Per Erlend Torbergsen Voie ◽  
Jan Høgsberg ◽  
Nils Sødahl
Keyword(s):  
Hybrid Method ◽  
Time Domain ◽  
Computation Time ◽  
Mooring Line ◽  
Mooring Lines ◽  
Fem Model ◽  
Input Variables ◽  
The Time Domain ◽  
The Cost ◽  
Short Time

Dynamic analyses of slender marine structures are computationally expensive. Recently it has been shown how a hybrid method which combines FEM models and artificial neural networks (ANN) can be used to reduce the computation time spend on the time domain simulations associated with fatigue analysis of mooring lines by two orders of magnitude. The present study shows how an ANN trained to perform nonlinear dynamic response simulation can be optimized using a method known as optimal brain damage (OBD) and thereby be used to rank the importance of all analysis input. Both the training and the optimization of the ANN are based on one short time domain simulation sequence generated by a FEM model of the structure. This means that it is possible to evaluate the importance of input parameters based on this single simulation only. The method is tested on a numerical model of mooring lines on a floating off-shore installation. It is shown that it is possible to estimate the cost of ignoring one or more input variables in an analysis.

Time Domain Simulations on a Single Point Moored Submerged Sphere of Variable Radius

2005 ◽  
Author(s):  
Joa˜o M. B. P. Cruz ◽  
Anto´nio J. N. A. Sarmento
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Physical Phenomenon ◽  
Single Point ◽  
Vertical Direction ◽  
Equation Of Motion ◽  
Hydrodynamic Coefficients ◽  
Energy Converter ◽  
Submerged Sphere ◽  
The Time Domain

This paper presents a different approach to the work developed by Cruz and Sarmento (2005), where the same problem was studied in the frequency domain. It concerns the same sphere, connected to the seabed by a tension line (single point moored), that oscillates with respect to the vertical direction in the plane of wave propagation. The pulsating nature of the sphere is the basic physical phenomenon that allows the use of this model as a simulation of a floating wave energy converter. The hydrodynamic coefficients and diffraction forces presented in Linton (1991) and Lopes and Sarmento (2002) for a submerged sphere are used. The equation of motion in the angular direction is solved in the time domain without any assumption about its output, allowing comparisons with the previously obtained results.

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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