The aim of this work is to develop a direct and exact approach using the Green's functions to control the steady-state transverse vibration of an axially moving double-string system supported by two rollers (eyelets) at both ends. The two strings are similar and coupled by a viscoelastic layer of a Kelvin–Voigt type. The control is achieved by introducing suitable control forces (using actuators) or passive elements to be located at some chosen locations along the span between the eyelets. A scheme is proposed for evaluating the control forces and their locations to suppress the vibration of the system and correspondingly decrease the generated noise. The variation of the running speed and different end supports are taken into consideration.
AbrateS (1992) Vibration of belts and belt drives. Mechanism and Machine Theory. 27: 645–659.
2.
ArchibaldFREmslieAG (1958) The vibration of an axially accelerating string. ASME Applied Mechanics. 25: 347–348.
3.
ChungCHTanCA (1995) Active vibration control of the axially moving string by wave cancellation. Journal of Vibration and Acoustics. 117: 49–55.
4.
FodaMAAlsaifKA (2009) Control of lateral and angular vibrations at desired locations along vibrating beams. Journal of Vibration and Control. 15: 649–1678.
5.
FodaMA (2011) Vibration suppression of an axially moving string. Journal of Vibration and Control. 18: 58–75.
6.
Horssen vonWTPonomarevaSV (2005) On the construct of the solution of an equation describing an axially moving string. Journal of Sound and Vibration. 287: 359–366.
7.
KuklaS (1994) Free vibration of the system of two beams connected by many translational springs. Journal of Sound and Vibration. 172: 130–135.
8.
LeeSYMoteCDJr (1996) Vibration control of an axially moving string by boundary control. Journal of Dynamic System, Measurement, and Control. 118: 66–74.
9.
LiTHouZ (2006) Exponential stabilization of an axially moving string with geometrical nonlinearity by linear boundary feedback. Journal of Sound and Vibration. 296: 861–870.
10.
MahalingamS (1957) Transverse vibration of power transmission chain. British Journal of Applied Physics. 8: 145–148.
11.
MeirovitchL (2001) Fundamentals of Vibrations. New York: McGraw-Hill.
12.
MoteCD (1965) A study of band saw vibrations. Journal of the Franklin Institute. 279: 430–444.
13.
OniszczukZ (2000a) Transverse vibrations of elastically connected double-string complex system Part I: Free vibrations. Journal of Sound and Vibration. 232: 336–355.
14.
OniszczukZ (2000b) Transverse vibrations of elastically connected double-string complex system. Part II: Forced vibrations. Journal of Sound and Vibration. 232: 367–386.
15.
OniszczukZ (2000c) Free transverse vibrations of an elastically connected simply supported double-beam complex system. Journal of Sound and Vibration. 232: 387–403.
16.
OniszczukZ (2003a) Damped vibration analysis of an elastically connected complex double-string system. Journal of Sound and Vibration. 264: 253–271.
17.
OniszczukZ (2003b) Forced transverse vibrations of an elastically connected complex simply supported double-beam system. Journal of Sound and Vibration. 264: 273–286.
18.
RoachG (1981) Greens Functions. Cambridge, UK: Cambridge University Press.
19.
RusinJŚniadyPŚniadyP (2011) Vibrations of double-string complex system under moving forces. Closed solutions. Journal of Sound and Vibration. 330: 404–415.
20.
TanCAYingS (2000) Active control of the axially moving string: Theory and experiment. Journal of Sound and Vibration. 236: 861–880.
21.
WickertJAMoteCDJr (1988) Current research on the vibration and stability of axially-moving materials. The Shock and Vibration Digest. 30: 3–13.
22.
VuHVOrdonezAMKarnoppBH (2000) Vibration of a double-beam system. Journal of Sound and Vibration. 229: 807–822.
23.
YangK-JHongK-SMatsunoF (2004) Robust adaptive boundary control of an axially moving string under spatiotemporally varying tension. Journal of Sound and Vibration. 273: 1007–1029.
24.
ZhuWDMoteCDJr (1995) Propagation of boundary disturbances in an axially moving strip in contact with rigid and flexible constraints. Journal of Applied Mechanics. 62: 873–879.
25.
ZhangYLuQYWangSLLiuX (2008) Vibration and buckling of a double-beam system under compressive axial loading. Journal of Sound and Vibration. 318: 341–352.
