References
- Marynowski K, Kapitaniak T. Dynamics of axially moving continua. Int J Mech Sci. 2014;81:26–41.
- Hong KS, Pham PT. Control of axially moving systems: a review. Int J Control Autom Syst. 2019;17(12):2983–3008.
- Chen LQ. Analysis and control of transverse vibrations of axially moving strings. Appl Mech Rev. 2005;58(2):91–116.
- Miranker WL. The wave equation in a medium in motion. IBM J Res Dev. 1960;4(1):36–42.
- Mote CD. A study of band saw vibrations. J Franklin Inst. 1965;279(6):430–444.
- Tan CA, Ying S. Dynamic analysis of the axially moving string based on wave propagation. ASME J Appl Mech. 1997;64(2):394–400.
- Chen EW, Ferguson NS. Analysis of energy dissipation in an elastic moving string with a viscous damper at one end. J Sound Vib. 2014;333(9):2556–2570.
- Chen E, He Y, Zhang K, et al. A superposition method of reflected wave for moving string vibration with nonclassical boundary. J Chin Inst Eng. 2019;42(4):327–332.
- Chen E, Yuan J, Ferguson N, et al. A wave solution for energy dissipation and exchange at nonclassical boundaries of a traveling string. Mech Syst Signal Process. 2021;150:107272.
- Lee SY, Mote CD. Vibration control of an axially moving string by boundary control. J Dyn Syst Meas Control. 1996;118(1):66–74.
- Gaiko NV, van Horssen WT. On the transverse, low frequency vibrations of a traveling string with boundary damping. J Vib Acoust. 2015;137(4):041004 (10p).
- Ghenimi S, Sengouga A. Free vibrations of axially moving strings: energy estimates and boundary observability. 2022. http://arxiv.org/abs/2201.01866.
- Fung RF, Wu JW, Wu SL. Exponential stabilization of an axially moving string by linear boundary feedback. Automatica. 1999;35(1):177–181.
- Veselić K. On linear vibrational systems with one dimensional damping. Appl Anal. 1988;29(1-2):1–18.
- Cox S, Zuazua E. The rate at which energy decays in a string damped at one end. Indiana Univ Math J. 1995;44(2):545–573.
- Cherkaoui M. Estimation optimale du taux de décroissance de l'énergie pour une équation des ondes avec contrôle frontière. INRIA; 1994. (Research Report RR-2328). Available at https://hal.inria.fr/inria-00074346.
- Quinn JP, Russell DL. Asymptotic stability and energy decay rates for solutions of hyperbolic equations with boundary damping. Proc R Soc Edinb A Math. 1977;77(1-2):97–127.
- Sengouga A. Exact boundary observability and controllability of the wave equation in an interval with two moving endpoints. Evol Equ Control Theory. 2020;9(1):1–25.
- McIver DB. Hamilton's principle for systems of changing mass. J Eng Math. 1973;7(3):249–261.
- Cassel KW. Variational methods with applications in science and engineering. New York, USA: Cambridge University Press; 2013.