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Volumn 38, Issue 6, 2003, Pages 851-872

Resonant non-linear normal modes. Part I: Analytical treatment for structural one-dimensional systems

Author keywords

Internal resonance; Method of multiple scales; Non linear normal mode; Non linear orthogonality; Virtual work

Indexed keywords

APPROXIMATION THEORY; DISTRIBUTED PARAMETER CONTROL SYSTEMS; GALERKIN METHODS; PHASE MODULATION; RESONANCE;

EID: 0037411955     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(02)00033-1     Document Type: Article
Times cited : (181)

References (24)
  • 1
    • 0031259358 scopus 로고    scopus 로고
    • Experimental investigation of the non-linear response of a hanging cable. Part I: Local analysis
    • Rega G., Alaggio R., Benedettini F. Experimental investigation of the non-linear response of a hanging cable. Part I: local analysis. Nonlinear Dynamics. 14:1997;89.
    • (1997) Nonlinear Dynamics , vol.14 , pp. 89
    • Rega, G.1    Alaggio, R.2    Benedettini, F.3
  • 3
    • 0001213074 scopus 로고
    • The normal modes of nonlinear N -degree-of-freedom systems
    • Rosenberg R.M. The normal modes of nonlinear. N -degree-of-freedom systems J. Appl. Mech. 30:1962;7.
    • (1962) J. Appl. Mech. , vol.30 , pp. 7
    • Rosenberg, R.M.1
  • 4
    • 0028461550 scopus 로고
    • An energy-based formulation for computing nonlinear normal modes in undamped continuous systems
    • King M.E., Vakakis A.F. An energy-based formulation for computing nonlinear normal modes in undamped continuous systems. J. Vibr. Acoustics. 116:1993;332.
    • (1993) J. Vibr. Acoustics , vol.116 , pp. 332
    • King, M.E.1    Vakakis, A.F.2
  • 5
    • 0001313559 scopus 로고    scopus 로고
    • An energy-based approach to computing resonant nonlinear normal modes
    • King M.E., Vakakis A.F. An energy-based approach to computing resonant nonlinear normal modes. J. Appl. Mech. 63:1996;810.
    • (1996) J. Appl. Mech. , vol.63 , pp. 810
    • King, M.E.1    Vakakis, A.F.2
  • 6
    • 0028203123 scopus 로고
    • Normal modes of vibration for nonlinear continuous systems
    • Shaw S.W., Pierre C. Normal modes of vibration for nonlinear continuous systems. J. Sound Vibr. 169:1994;319.
    • (1994) J. Sound Vibr. , vol.169 , pp. 319
    • Shaw, S.W.1    Pierre, C.2
  • 7
    • 0000992329 scopus 로고
    • Non-linear modal analysis of structural systems featuring internal resonances
    • Boivin N., Pierre C., Shaw S.W. Non-linear modal analysis of structural systems featuring internal resonances. J. Sound Vibr. 182:1995;336.
    • (1995) J. Sound Vibr. , vol.182 , pp. 336
    • Boivin, N.1    Pierre, C.2    Shaw, S.W.3
  • 8
    • 0029402739 scopus 로고
    • On direct methods for constructing nonlinear normal modes of continuous systems
    • Nayfeh A.H. On direct methods for constructing nonlinear normal modes of continuous systems. J. Vibr. Control. 1:1995;389.
    • (1995) J. Vibr. Control , vol.1 , pp. 389
    • Nayfeh, A.H.1
  • 9
    • 0030193842 scopus 로고    scopus 로고
    • On nonlinear normal modes of systems with internal resonance
    • Nayfeh A.H., Chin C.-M., Nayfeh S.A. On nonlinear normal modes of systems with internal resonance. J. Vibr. Acoustics. 118:1996;340.
    • (1996) J. Vibr. Acoustics , vol.118 , pp. 340
    • Nayfeh, A.H.1    Chin, C.-M.2    Nayfeh, S.A.3
  • 10
    • 0032655393 scopus 로고    scopus 로고
    • Nonlinear normal modes of buckled beams: Three-to-one and one-to-one internal resonances
    • Nayfeh A.H., Lacarbonara W., Chin C.-M. Nonlinear normal modes of buckled beams. Three-to-one and one-to-one internal resonances Nonlinear Dynamics. 18:1999;253.
    • (1999) Nonlinear Dynamics , vol.18 , pp. 253
    • Nayfeh, A.H.1    Lacarbonara, W.2    Chin, C.-M.3
  • 11
    • 0011696761 scopus 로고    scopus 로고
    • Resonant non-linear normal modes. Part II: Activation/orthogonality conditions for shallow structural systems
    • W. Lacarbonara, G. Rega, Resonant non-linear normal modes. Part II: activation/orthogonality conditions for shallow structural systems, Int. J. Non-Linear Mech. 37 (2002).
    • (2002) Int. J. Non-Linear Mech. , vol.37
    • Lacarbonara, W.1    Rega, G.2
  • 12
    • 0001786839 scopus 로고
    • On the discretization of weakly nonlinear spatially continuous systems
    • W. Kliemann, N. Sri Namachchivaya (Eds.), CRC Press, Boca Raton, FL
    • A.H. Nayfeh, S.A. Nayfeh, M. Pakdemirli, On the discretization of weakly nonlinear spatially continuous systems, in: W. Kliemann, N. Sri Namachchivaya (Eds.), Nonlinear Dynamics and Stochastic Mechanics, CRC Press, Boca Raton, FL, 1995, p. 175.
    • (1995) Nonlinear Dynamics and Stochastic Mechanics , pp. 175
    • Nayfeh, A.H.1    Nayfeh, S.A.2    Pakdemirli, M.3
  • 13
    • 0001238155 scopus 로고    scopus 로고
    • Vibrations of continuous systems having arbitrary quadratic and cubic nonlinearities
    • Pakdemirli M., Boyaci H. Vibrations of continuous systems having arbitrary quadratic and cubic nonlinearities. Appl. Mech. Eng. 1:1996;445.
    • (1996) Appl. Mech. Eng. , vol.1 , pp. 445
    • Pakdemirli, M.1    Boyaci, H.2
  • 14
    • 0001742916 scopus 로고    scopus 로고
    • Direct treatment and discretizations of nonlinear spatially continuous systems
    • Lacarbonara W. Direct treatment and discretizations of nonlinear spatially continuous systems. J. Sound Vibr. 221:1999;849.
    • (1999) J. Sound Vibr. , vol.221 , pp. 849
    • Lacarbonara, W.1
  • 15
    • 0001339289 scopus 로고
    • A variational method for weak resonant wave interactions
    • Simmons W.F. A variational method for weak resonant wave interactions. Proc. Roy. Soc. A. 309:1969;551.
    • (1969) Proc. Roy. Soc. A , vol.309 , pp. 551
    • Simmons, W.F.1
  • 16
    • 0028387071 scopus 로고
    • A comparison of two perturbation methods for vibrations of systems with quadratic and cubic nonlinearities
    • Pakdemirli M. A comparison of two perturbation methods for vibrations of systems with quadratic and cubic nonlinearities. Mech. Res. Commun. 21:1994;203.
    • (1994) Mech. Res. Commun. , vol.21 , pp. 203
    • Pakdemirli, M.1
  • 17
    • 0032097205 scopus 로고    scopus 로고
    • Reduced-order models of weakly nonlinear spatially continuous systems
    • Nayfeh A.H. Reduced-order models of weakly nonlinear spatially continuous systems. Nonlinear Dynamics. 16:1998;105.
    • (1998) Nonlinear Dynamics , vol.16 , pp. 105
    • Nayfeh, A.H.1
  • 20
    • 0029277202 scopus 로고
    • Symmetries of the amplitude equations of an inextensional beam with internal resonance
    • Feng Z.C., Leal L.G. Symmetries of the amplitude equations of an inextensional beam with internal resonance. J. Appl. Mech. 62:1994;235.
    • (1994) J. Appl. Mech. , vol.62 , pp. 235
    • Feng, Z.C.1    Leal, L.G.2
  • 21
    • 0001607691 scopus 로고
    • The linear theory of free vibrations of a suspended cable
    • Irvine H.M., Caughey T.K. The linear theory of free vibrations of a suspended cable. Proc. Roy. Soc. London, Ser. A. 341:1974;299.
    • (1974) Proc. Roy. Soc. London, Ser. A , vol.341 , pp. 299
    • Irvine, H.M.1    Caughey, T.K.2
  • 23
    • 0023044651 scopus 로고
    • Comments on curve veering in eigenvalue problems
    • Perkins N.C., Mote C.D. Jr. Comments on curve veering in eigenvalue problems. J. Sound Vibr. 106:1986;451.
    • (1986) J. Sound Vibr. , vol.106 , pp. 451
    • Perkins, N.C.1    Mote C.D., Jr.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.