메뉴 건너뛰기




Volumn 67, Issue 3, 2010, Pages 205-218

Asymptotic analysis on nonlinear vibration of axially accelerating viscoelastic strings with the standard linear solid model

Author keywords

Asymptotic perturbation; Axially accelerating string; Nonlinearity; Parametric vibration; Viscoelasticity

Indexed keywords

ANALYTICAL APPROACH; ASYMPTOTIC PERTURBATION; CO-ORDINATE TRANSFORMATION; EXISTENCE CONDITIONS; FIXED POINTS; GOVERNING EQUATIONS; INITIAL STRESS; KIRCHHOFF; MATERIAL PARAMETER; MATERIAL TIME DERIVATIVE; MODULATION EQUATIONS; NON-LINEAR VIBRATIONS; NON-LINEARITY; NUMERICAL RESULTS; PARAMETRIC VIBRATIONS; PRINCIPAL PARAMETRIC RESONANCE; SOLVABILITY CONDITIONS; SPEED FLUCTUATIONS; STANDARD LINEAR SOLID MODELS; STEADY-STATE RESPONSE; TRANSVERSE MOTIONS; VISCOELASTIC BEHAVIORS; VISCOELASTIC STRINGS;

EID: 77953326525     PISSN: 00220833     EISSN: 15732703     Source Type: Journal    
DOI: 10.1007/s10665-009-9316-9     Document Type: Article
Times cited : (21)

References (48)
  • 1
    • 25844516751 scopus 로고    scopus 로고
    • Analysis and control of transverse vibrations of axially moving strings
    • Chen LQ (2005) Analysis and control of transverse vibrations of axially moving strings. Appl Mech Rev 58: 91-116.
    • (2005) Appl Mech Rev , vol.58 , pp. 91-116
    • Chen, L.Q.1
  • 2
    • 0000642570 scopus 로고    scopus 로고
    • Nonlinear vibrations of viscoelastic moving belts, part 1: Free vibration analysis
    • Zhang L, Zu JW (1998) Nonlinear vibrations of viscoelastic moving belts, part 1: free vibration analysis. J Sound Vib 216: 75-91.
    • (1998) J Sound Vib , vol.216 , pp. 75-91
    • Zhang, L.1    Zu, J.W.2
  • 3
    • 0036721960 scopus 로고    scopus 로고
    • Nonlinear free oscillations of moving belts
    • Hou Z, Zu JW (2002) Nonlinear free oscillations of moving belts. Mech Mach Theory 37: 925-940.
    • (2002) Mech Mach Theory , vol.37 , pp. 925-940
    • Hou, Z.1    Zu, J.W.2
  • 4
    • 0001923273 scopus 로고    scopus 로고
    • Nonlinear vibrations of viscoelastic moving belts, part 2: Forced vibration analysis
    • Zhang L, Zu JW (1998) Nonlinear vibrations of viscoelastic moving belts, part 2: forced vibration analysis. J Sound Vib 216: 93-105.
    • (1998) J Sound Vib , vol.216 , pp. 93-105
    • Zhang, L.1    Zu, J.W.2
  • 5
    • 0031102079 scopus 로고    scopus 로고
    • The transient amplitude of the viscoelastic travelling string: An integral constitutive law
    • Fung RF, Huang JS, Chen YC (1997) The transient amplitude of the viscoelastic travelling string: an integral constitutive law. J Sound Vib 201: 153-167.
    • (1997) J Sound Vib , vol.201 , pp. 153-167
    • Fung, R.F.1    Huang, J.S.2    Chen, Y.C.3
  • 6
    • 0032019860 scopus 로고    scopus 로고
    • Nonlinear dynamic analysis of the viscoelastic string with a harmonically varying transport speed
    • Fung RF, Huang JS, Chen YC, Yao CM (1998) Nonlinear dynamic analysis of the viscoelastic string with a harmonically varying transport speed. Comput Struct 66: 777-784.
    • (1998) Comput Struct , vol.66 , pp. 777-784
    • Fung, R.F.1    Huang, J.S.2    Chen, Y.C.3    Yao, C.M.4
  • 7
    • 0033149346 scopus 로고    scopus 로고
    • Nonlinear vibration of parametrically excited moving belts, part I: Dynamic response
    • Zhang L, Zu JW (1999) Nonlinear vibration of parametrically excited moving belts, part I: dynamic response. ASME J Appl Mech 66: 396-402.
    • (1999) ASME J Appl Mech , vol.66 , pp. 396-402
    • Zhang, L.1    Zu, J.W.2
  • 8
    • 0033148490 scopus 로고    scopus 로고
    • Nonlinear vibration of parametrically excited moving belts, part II: Stability analysis
    • Zhang L, Zu JW (1999) Nonlinear vibration of parametrically excited moving belts, part II: stability analysis. ASME J Appl Mech 66: 403-409.
    • (1999) ASME J Appl Mech , vol.66 , pp. 403-409
    • Zhang, L.1    Zu, J.W.2
  • 9
    • 0038370704 scopus 로고    scopus 로고
    • Transient response for viscoelastic moving belts using block-by-block method
    • Zhang L, Zu JW, Zhong Z (2002) Transient response for viscoelastic moving belts using block-by-block method. Int J Struct Stab Dyn 2: 265-280.
    • (2002) Int J Struct Stab Dyn , vol.2 , pp. 265-280
    • Zhang, L.1    Zu, J.W.2    Zhong, Z.3
  • 10
    • 0038548439 scopus 로고    scopus 로고
    • Dynamic response of the parametrically excited axially moving string constituted by the Boltzmann superposition principle
    • Chen LQ, Zu JW, Wu J (2003) Dynamic response of the parametrically excited axially moving string constituted by the Boltzmann superposition principle. Acta Mech 162: 143-155.
    • (2003) Acta Mech , vol.162 , pp. 143-155
    • Chen, L.Q.1    Zu, J.W.2    Wu, J.3
  • 11
    • 0037417263 scopus 로고    scopus 로고
    • The regular and chaotic vibrations of an axially moving viscoelastic string based on 4-order Galerkin truncation
    • Chen LQ, Zhang NH, Zu JW (2003) The regular and chaotic vibrations of an axially moving viscoelastic string based on 4-order Galerkin truncation. J Sound Vib 261: 764-773.
    • (2003) J Sound Vib , vol.261 , pp. 764-773
    • Chen, L.Q.1    Zhang, N.H.2    Zu, J.W.3
  • 12
    • 54049112486 scopus 로고    scopus 로고
    • Dynamic responses of viscoelastic axially moving belt
    • Li YH, Gao Q, Jian KL, Yin XG (2003) Dynamic responses of viscoelastic axially moving belt. Appl Math Mech 24: 1348-1354.
    • (2003) Appl Math Mech , vol.24 , pp. 1348-1354
    • Li, Y.H.1    Gao, Q.2    Jian, K.L.3    Yin, X.G.4
  • 13
    • 6344235287 scopus 로고    scopus 로고
    • Transient responses of an axially accelerating viscoelastic string constituted by a fractional differentiation law
    • Chen LQ, Zhao WJ, Zu JW (2004) Transient responses of an axially accelerating viscoelastic string constituted by a fractional differentiation law. J Sound Vib 278: 861-871.
    • (2004) J Sound Vib , vol.278 , pp. 861-871
    • Chen, L.Q.1    Zhao, W.J.2    Zu, J.W.3
  • 14
    • 3142752741 scopus 로고    scopus 로고
    • Asymptotic nonlinear behaviors in transverse vibration of an axially accelerating viscoelastic string
    • Chen LQ, Wu J, Zu JW (2004) Asymptotic nonlinear behaviors in transverse vibration of an axially accelerating viscoelastic string. Nonlinear Dyn 35: 347-360.
    • (2004) Nonlinear Dyn , vol.35 , pp. 347-360
    • Chen, L.Q.1    Wu, J.2    Zu, J.W.3
  • 15
    • 1342332025 scopus 로고    scopus 로고
    • Transverse vibrations of an axially accelerating viscoelastic string with geometric nonlinearity
    • Chen LQ, Zu JW, Wu J, Yang XD (2004) Transverse vibrations of an axially accelerating viscoelastic string with geometric nonlinearity. J Eng Math 48: 171-182.
    • (2004) J Eng Math , vol.48 , pp. 171-182
    • Chen, L.Q.1    Zu, J.W.2    Wu, J.3    Yang, X.D.4
  • 16
    • 1142304474 scopus 로고    scopus 로고
    • The chaotic response of the viscoelastic traveling string: An integral constitutive law
    • Chen LQ, Wu J, Zu JW (2004) The chaotic response of the viscoelastic traveling string: an integral constitutive law. Chaos Solitons Fractals 21: 349-357.
    • (2004) Chaos Solitons Fractals , vol.21 , pp. 349-357
    • Chen, L.Q.1    Wu, J.2    Zu, J.W.3
  • 17
    • 9644310364 scopus 로고    scopus 로고
    • A numerical method for simulating transverse vibrations of axially moving strings
    • Chen LQ, Zhao WJ (2005) A numerical method for simulating transverse vibrations of axially moving strings. Appl Math Comput 160: 411-422.
    • (2005) Appl Math Comput , vol.160 , pp. 411-422
    • Chen, L.Q.1    Zhao, W.J.2
  • 18
    • 20444470221 scopus 로고    scopus 로고
    • Nonlinear vibration of parametrically excited, viscoelastic, axially moving strings
    • Mockensturm EM, Guo JP (2005) Nonlinear vibration of parametrically excited, viscoelastic, axially moving strings. ASME J Appl Mech 72: 374-380.
    • (2005) ASME J Appl Mech , vol.72 , pp. 374-380
    • Mockensturm, E.M.1    Guo, J.P.2
  • 19
    • 33750715682 scopus 로고    scopus 로고
    • Principal parametric resonance of axially accelerating viscoelastic strings constituted by the Boltzmann superposition principle
    • Chen LQ (2005) Principal parametric resonance of axially accelerating viscoelastic strings constituted by the Boltzmann superposition principle. Proc R Soc Lond A 461: 2701-2720.
    • (2005) Proc R Soc Lond A , vol.461 , pp. 2701-2720
    • Chen, L.Q.1
  • 20
    • 27144444047 scopus 로고    scopus 로고
    • Multi pulse orbits and chaotic dynamics in motion of parametrically excited viscoelastic moving belt
    • Zhang W, Yao MH (2006) Multi pulse orbits and chaotic dynamics in motion of parametrically excited viscoelastic moving belt. Chaos Solitons Fractals 28: 42-66.
    • (2006) Chaos Solitons Fractals , vol.28 , pp. 42-66
    • Zhang, W.1    Yao, M.H.2
  • 21
    • 38049148375 scopus 로고    scopus 로고
    • Complex mode Galerkin approach in transverse vibration of an axially accelerating viscoelastic string
    • Zhang NH, Wang JJ, Cheng CJ (2007) Complex mode Galerkin approach in transverse vibration of an axially accelerating viscoelastic string. Appl Math Mech 28: 1-9.
    • (2007) Appl Math Mech , vol.28 , pp. 1-9
    • Zhang, N.H.1    Wang, J.J.2    Cheng, C.J.3
  • 22
    • 33947097402 scopus 로고    scopus 로고
    • Nonlinear dynamic behavior of a moving viscoelastic string undergoing three-dimensional vibration
    • Ha JL, Chang JR, Fung RF (2007) Nonlinear dynamic behavior of a moving viscoelastic string undergoing three-dimensional vibration. Chaos Solitons Fractals 33: 1117-1134.
    • (2007) Chaos Solitons Fractals , vol.33 , pp. 1117-1134
    • Ha, J.L.1    Chang, J.R.2    Fung, R.F.3
  • 23
    • 34548574661 scopus 로고    scopus 로고
    • Dynamic analysis of an axially moving viscoelastic string by the Galerkin method using translating string eigenfunctions
    • Zhang NH (2008) Dynamic analysis of an axially moving viscoelastic string by the Galerkin method using translating string eigenfunctions. Chaos Solitons Fractals 35: 291-302.
    • (2008) Chaos Solitons Fractals , vol.35 , pp. 291-302
    • Zhang, N.H.1
  • 24
    • 34248397659 scopus 로고    scopus 로고
    • Modeling of nonlinear oscillations for viscoelastic moving belt using generalized Hamilton's principle
    • Chen LH, Zhang W, Liu YQ (2007) Modeling of nonlinear oscillations for viscoelastic moving belt using generalized Hamilton's principle. ASME J Vib Acoust 129: 128-132.
    • (2007) ASME J Vib Acoust , vol.129 , pp. 128-132
    • Chen, L.H.1    Zhang, W.2    Liu, Y.Q.3
  • 25
    • 0036778875 scopus 로고    scopus 로고
    • Kelvin-Voigt versus Burgers internal damping in modeling of axially moving viscoelastic web
    • Marynowski K, Kapitaniak T (2002) Kelvin-Voigt versus Burgers internal damping in modeling of axially moving viscoelastic web. Int J Non-Linear Mech 37: 1147-1161.
    • (2002) Int J Non-Linear Mech , vol.37 , pp. 1147-1161
    • Marynowski, K.1    Kapitaniak, T.2
  • 26
    • 1142280266 scopus 로고    scopus 로고
    • Non-linear vibrations of an axially moving viscoelastic web with time-dependent tension
    • Marynowski K (2004) Non-linear vibrations of an axially moving viscoelastic web with time-dependent tension. Chaos Solitons Fractals 21: 481-490.
    • (2004) Chaos Solitons Fractals , vol.21 , pp. 481-490
    • Marynowski, K.1
  • 27
    • 33748874885 scopus 로고    scopus 로고
    • Two-dimensional rheological element in modeling of axially moving viscoelastic web
    • Marynowski K (2006) Two-dimensional rheological element in modeling of axially moving viscoelastic web. Eur J Mech A 25: 729-744.
    • (2006) Eur J Mech A , vol.25 , pp. 729-744
    • Marynowski, K.1
  • 28
    • 34247399622 scopus 로고    scopus 로고
    • Zener internal damping in modeling of axially moving viscoelastic beam with time-dependent tension
    • Marynowski K, Kapitaniak T (2007) Zener internal damping in modeling of axially moving viscoelastic beam with time-dependent tension. Int J Non-Linear Mech 42: 118-131.
    • (2007) Int J Non-Linear Mech , vol.42 , pp. 118-131
    • Marynowski, K.1    Kapitaniak, T.2
  • 31
    • 5644239856 scopus 로고    scopus 로고
    • Asymptotic approaches in mechanics: New parameters and procedures
    • Andrianov IV, Awrejcewicz J, Barantsev RG (2003) Asymptotic approaches in mechanics: new parameters and procedures. Appl Mech Rev 56: 87-110.
    • (2003) Appl Mech Rev , vol.56 , pp. 87-110
    • Andrianov, I.V.1    Awrejcewicz, J.2    Barantsev, R.G.3
  • 32
    • 0032157865 scopus 로고    scopus 로고
    • On mode interactions for a weakly nonlinear beam equation
    • Boertjens GJ, van Horssen WT (1998) On mode interactions for a weakly nonlinear beam equation. Nonlinear Dyn 12: 23-40.
    • (1998) Nonlinear Dyn , vol.12 , pp. 23-40
    • Boertjens, G.J.1    van Horssen, W.T.2
  • 33
    • 0032688439 scopus 로고    scopus 로고
    • The asymptotic perturbation method for nonlinear continuous systems
    • Maccari A (1999) The asymptotic perturbation method for nonlinear continuous systems. Nonlinear Dyn 19: 1-18.
    • (1999) Nonlinear Dyn , vol.19 , pp. 1-18
    • Maccari, A.1
  • 34
    • 0034566366 scopus 로고    scopus 로고
    • An asymptotic theory for a weakly nonlinear beam equation with a quadratic perturbation
    • Boertjens GJ, van Horssen WT (2000) An asymptotic theory for a weakly nonlinear beam equation with a quadratic perturbation. SIAM J Appl Math 60: 602-632.
    • (2000) SIAM J Appl Math , vol.60 , pp. 602-632
    • Boertjens, G.J.1    van Horssen, W.T.2
  • 35
    • 0034247066 scopus 로고    scopus 로고
    • On interactions of oscillation modes for a weakly nonlinear undamped elastic beam with an external force
    • Boertjens GJ, van Horssen WT (2000) On interactions of oscillation modes for a weakly nonlinear undamped elastic beam with an external force. J Sound Vib 235: 201-217.
    • (2000) J Sound Vib , vol.235 , pp. 201-217
    • Boertjens, G.J.1    van Horssen, W.T.2
  • 36
    • 0033686534 scopus 로고    scopus 로고
    • Saddle-Node bifurcations of cycles in a relief valve
    • Maccari A (2000) Saddle-Node bifurcations of cycles in a relief valve. Nonlinear Dyn 22: 225-247.
    • (2000) Nonlinear Dyn , vol.22 , pp. 225-247
    • Maccari, A.1
  • 37
    • 0037122472 scopus 로고    scopus 로고
    • Asymptotic approach for nonlinear periodical vibrations of continuous structures
    • Andrianov IV, Danishevs'kyy VV (2002) Asymptotic approach for nonlinear periodical vibrations of continuous structures. J Sound Vib 249: 465-481.
    • (2002) J Sound Vib , vol.249 , pp. 465-481
    • Andrianov, I.V.1    Danishevs'kyy, V.V.2
  • 38
    • 33750700815 scopus 로고    scopus 로고
    • Some nonlinear dispersive waves arising in compressible hyperelastic plates
    • Chen RM (2006) Some nonlinear dispersive waves arising in compressible hyperelastic plates. Int J Eng Sci 44: 1188-1204.
    • (2006) Int J Eng Sci , vol.44 , pp. 1188-1204
    • Chen, R.M.1
  • 39
    • 51349132719 scopus 로고    scopus 로고
    • Asymptotic analysis of axially accelerating viscoelastic strings
    • Chen LQ, Chen H, Lim CW (2008) Asymptotic analysis of axially accelerating viscoelastic strings. Int J Eng Sci 46: 976-985.
    • (2008) Int J Eng Sci , vol.46 , pp. 976-985
    • Chen, L.Q.1    Chen, H.2    Lim, C.W.3
  • 40
    • 0003663640 scopus 로고
    • Vorlesungen ueber Mathematische Physik: Mechanik
    • von B. G. Teubner, Leipzig
    • Kirchhoff G (1877) Vorlesungen ueber Mathematische Physik: Mechanik. Druck und Verlag, von B. G. Teubner, Leipzig.
    • (1877) Druck und Verlag
    • Kirchhoff, G.1
  • 41
    • 0001345843 scopus 로고
    • Nonlinear-Linear vibration of a traveling tensioned beam
    • Wickert JA (1992) Nonlinear-Linear vibration of a traveling tensioned beam. Int J Non-Linear Mech 27: 503-517.
    • (1992) Int J Non-Linear Mech , vol.27 , pp. 503-517
    • Wickert, J.A.1
  • 42
    • 0031555838 scopus 로고    scopus 로고
    • Nonlinear vibration of power transmission belts
    • Moon J, Wickert JA (1997) Nonlinear vibration of power transmission belts. J Sound Vib 200: 419-431.
    • (1997) J Sound Vib , vol.200 , pp. 419-431
    • Moon, J.1    Wickert, J.A.2
  • 43
    • 0030190395 scopus 로고    scopus 로고
    • Stability and limit cycles of parametrically excited, axially moving strings
    • Mockensturm EM, Perkins NC, Ulsoy AG (1996) Stability and limit cycles of parametrically excited, axially moving strings. ASME J Vib Acoust 188: 346-351.
    • (1996) ASME J Vib Acoust , vol.188 , pp. 346-351
    • Mockensturm, E.M.1    Perkins, N.C.2    Ulsoy, A.G.3
  • 44
    • 11744378207 scopus 로고
    • On the nonlinear oscillation of an axially moving string
    • Mote CDJr (1966) On the nonlinear oscillation of an axially moving string. ASME J Appl Mech 33: 463-464.
    • (1966) ASME J Appl Mech , vol.33 , pp. 463-464
    • Mote, C.1
  • 45
    • 0025492121 scopus 로고
    • Classical vibration analysis of axially moving continua
    • Wickert JA, Mote CDJr (1990) Classical vibration analysis of axially moving continua. ASME J Appl Mech 57: 738-744.
    • (1990) ASME J Appl Mech , vol.57 , pp. 738-744
    • Wickert, J.A.1    Mote, C.2
  • 46
    • 43449099784 scopus 로고    scopus 로고
    • On two nonlinear models of the transversely vibrating string
    • Chen LQ, Ding H (2008) On two nonlinear models of the transversely vibrating string. Arch Appl Mech 18: 321-328.
    • (2008) Arch Appl Mech , vol.18 , pp. 321-328
    • Chen, L.Q.1    Ding, H.2
  • 47
    • 61349086097 scopus 로고    scopus 로고
    • On two transverse nonlinear models of axially moving beams
    • Ding H, Chen LQ (2009) On two transverse nonlinear models of axially moving beams. Sci China Ser E: Tech Sci 52: 743-751.
    • (2009) Sci China Ser E: Tech Sci , vol.52 , pp. 743-751
    • Ding, H.1    Chen, L.Q.2
  • 48
    • 84855360956 scopus 로고    scopus 로고
    • Steady-state transverse response in planar vibration of axially moving viscoelastic beams
    • (accepted)
    • Chen LQ, Ding H (2009) Steady-state transverse response in planar vibration of axially moving viscoelastic beams. ASME J Vib Acoust (accepted).
    • (2009) ASME J Vib Acoust
    • Chen, L.Q.1    Ding, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.