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Volumn 63, Issue 3, 1996, Pages 810-819

An energy-based approach to computing resonant nonlinear normal modes

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EID: 0001313559     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.2823367     Document Type: Article
Times cited : (44)

References (29)
  • 1
    • 0026419989 scopus 로고
    • The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic structures, Part I: Simply supported and clamped-clamped beams
    • Benamar, R., Bennouna, M. M. K., and White, R. G., 1991, “The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic structures, Part I: Simply supported and clamped-clamped beams,” Journal of Sound and Vibration, Vol. 149, pp. 179-195.
    • (1991) Journal of Sound and Vibration , vol.149 , pp. 179-195
    • Benamar, R.1    Bennouna, M.M.K.2    White, R.G.3
  • 2
    • 0021758053 scopus 로고
    • The effects of large vibration amplitudes on the fundamental mode shape of a clamped-clamped uniform beam
    • Bennouna, M. M. K., and White, R. G, 1984, “The effects of large vibration amplitudes on the fundamental mode shape of a clamped-clamped uniform beam,” Journal of Sound and Vibration, Vol. 96, pp. 309-331.
    • (1984) Journal of Sound and Vibration , vol.96 , pp. 309-331
    • Bennouna, M.M.K.1    White, R.G.2
  • 4
    • 0025638281 scopus 로고
    • Analytical study of similar normal modes and their bifurcations in a class of strongly nonlinear systems
    • Caughey, T. K., Vakakis, A. F., and Sivo, J., 1990, “Analytical study of similar normal modes and their bifurcations in a class of strongly nonlinear systems,” International Journal of Non-Linear Mechanics, Vol.' 25, No. 5, pp. 521-533.
    • (1990) International Journal of Non-Linear Mechanics , vol.25 , Issue.5 , pp. 521-533
    • Caughey, T.K.1    Vakakis, A.F.2    Sivo, J.3
  • 5
    • 0000576420 scopus 로고
    • On the existence of periodic solutions and normal mode vibrations of nonlinear systems
    • Cooke, C. H., and Struble, R. A., 1966, “On the existence of periodic solutions and normal mode vibrations of nonlinear systems,” Quarterly of Applied Mathematics, Vol. 24, No. 3, pp. 177-193.
    • (1966) Quarterly of Applied Mathematics , vol.24 , Issue.3 , pp. 177-193
    • Cooke, C.H.1    Struble, R.A.2
  • 6
    • 0038937822 scopus 로고
    • Analytical and experimental aspects of nonlinear normal modes and nonlinear mode localization
    • Urbana, IL
    • King, M. E., 1995, “Analytical and experimental aspects of nonlinear normal modes and nonlinear mode localization,” Ph.D. Thesis, University of Illinois, Urbana, IL.
    • (1995) Ph.D. Thesis, University of Illinois
    • King, M.E.1
  • 7
    • 0028461550 scopus 로고
    • An Energy-Based Formulation for Computing Nonlinear Normal Modes in Undamped Continuous Systems, ASME
    • King, M. E., and Vakakis, A. F., 1994, “An Energy-Based Formulation for Computing Nonlinear Normal Modes in Undamped Continuous Systems,” ASME Journal of Vibration and Acoustics, Vol. 116, pp. 332-340.
    • (1994) Journal of Vibration and Acoustics , vol.116 , pp. 332-340
    • King, M.E.1    Vakakis, A.F.2
  • 8
    • 0029292094 scopus 로고
    • Asymptotic analysis of nonlinear mode localization in a class of coupled continuous structures
    • King, M. E., and Vakakis, A. F., 1995, “Asymptotic analysis of nonlinear mode localization in a class of coupled continuous structures,” Int. Journal of Solids and Structures, Vol. 32, No. 8-9, pp. 1161-1177.
    • (1995) Int. Journal of Solids and Structures , vol.32 , Issue.8-9 , pp. 1161-1177
    • King, M.E.1    Vakakis, A.F.2
  • 9
    • 0000405689 scopus 로고
    • On periodic solutions close to rectilinear normal vibration modes
    • Manevitch, L. I., and Mikhlin, Y. V., 1972, “On periodic solutions close to rectilinear normal vibration modes,” PMM, Vol. 36, No. 6, pp. 1051-1058.
    • (1972) PMM , vol.36 , Issue.6 , pp. 1051-1058
    • Manevitch, L.I.1    Mikhlin, Y.V.2
  • 10
    • 33746099584 scopus 로고
    • Resonance modes of near-conservative nonlinear systems
    • Mikhlin, Y. V., 1974, “Resonance modes of near-conservative nonlinear systems,” PMM, Vol. 38, No. 3, pp. 459-464.
    • (1974) PMM , vol.38 , Issue.3 , pp. 459-464
    • Mikhlin, Y.V.1
  • 11
    • 0007097754 scopus 로고
    • The Stability of Bifurcating Periodic Solutions in a Two Degree-of-Freedom Nonlinear System
    • Month, L. A., and Rand, R. H., 1977, “The Stability of Bifurcating Periodic Solutions in a Two Degree-of-Freedom Nonlinear System,” ASME Journal of Applied Mechanics, Vol. 44, pp. 782-783.
    • (1977) ASME Journal of Applied Mechanics , vol.44 , pp. 782-783
    • Month, L.A.1    Rand, R.H.2
  • 14
    • 0028197991 scopus 로고
    • On Nonlinear Modes of Continuous Systems, ASME
    • Nayfeh, A. H., and Nayfeh, S. A., 1994, “On Nonlinear Modes of Continuous Systems,” ASME Journal of Vibration and Acoustics, Vol. 116, pp. 129-136.
    • (1994) Journal of Vibration and Acoustics , vol.116 , pp. 129-136
    • Nayfeh, A.H.1    Nayfeh, S.A.2
  • 15
    • 0015110725 scopus 로고
    • A higher order approximation for Nonlinear Normal Modes in two-dof Systems
    • Rand, R. H., 1971, “A higher order approximation for Nonlinear Normal Modes in two-dof Systems,” International Journal of Non-Linear Mechanics, Vol. 6, pp. 545-547.
    • (1971) International Journal of Non-Linear Mechanics , vol.6 , pp. 545-547
    • Rand, R.H.1
  • 16
    • 85025205564 scopus 로고
    • personal communications with authors
    • Rand, R. H., 1995, personal communications with authors.
    • (1995)
    • Rand, R.H.1
  • 17
    • 0001394731 scopus 로고
    • Bifurcations of nonlinear normal modes in a class of two degree of freedom systems
    • Rand, R. H., Pak, C. H., and Vakakis, A. F., 1992, “Bifurcations of nonlinear normal modes in a class of two degree of freedom systems,” Acta Mechanica, [Suppl] Vol. 3, pp. 129-145.
    • (1992) Acta Mechanica , vol.3 , pp. 129-145
    • Rand, R.H.1    Pak, C.H.2    Vakakis, A.F.3
  • 18
    • 0006998795 scopus 로고
    • On the existence of normal mode vibrations of nonlinear systems with two degrees of freedom
    • Rosenberg, R. M., 1964, “On the existence of normal mode vibrations of nonlinear systems with two degrees of freedom,” Quarterly of Applied Mathematics, Vol. 22, No. 3, pp. 217-234.
    • (1964) Quarterly of Applied Mathematics , vol.22 , Issue.3 , pp. 217-234
    • Rosenberg, R.M.1
  • 19
    • 33645049419 scopus 로고
    • On non-linear vibrations of systems with many degrees of freedom
    • Rosenberg, R. M., 1966, “On non-linear vibrations of systems with many degrees of freedom,” Advances in Applied Mechanics, Vol. 9, pp. 155-242.
    • (1966) Advances in Applied Mechanics , vol.9 , pp. 155-242
    • Rosenberg, R.M.1
  • 20
    • 0026420003 scopus 로고
    • Nonlinear normal modes and invariant manifolds
    • Shaw, S. W., and Pierre, C., 1991, “Nonlinear normal modes and invariant manifolds,” Journal of Sound and Vibration, Vol. 150, pp. 170-173.
    • (1991) Journal of Sound and Vibration , vol.150 , pp. 170-173
    • Shaw, S.W.1    Pierre, C.2
  • 22
    • 0027911991 scopus 로고
    • Normal modes for nonlinear vibratory systems
    • Shaw, S. W., and Pierre, C., 1993, “Normal modes for nonlinear vibratory systems,” Journal of Sound and Vibration, Vol. 164, No. 1, pp. 85-96.
    • (1993) Journal of Sound and Vibration , vol.164 , Issue.1 , pp. 85-96
    • Shaw, S.W.1    Pierre, C.2
  • 23
    • 0028203123 scopus 로고
    • Normal modes of vibration for nonlinear continuous systems
    • Shaw, S. W., and Pierre, C., 1994, “Normal modes of vibration for nonlinear continuous systems,” Journal of Sound and Vibration, Vol. 169, No. 3, pp. 319-348.
    • (1994) Journal of Sound and Vibration , vol.169 , Issue.3 , pp. 319-348
    • Shaw, S.W.1    Pierre, C.2
  • 24
    • 0003966737 scopus 로고
    • Analysis and identification of linear and nonlinear normal modes in vibrating systems
    • Pasadena, CA
    • Vakakis, A. F., 1990, “Analysis and identification of linear and nonlinear normal modes in vibrating systems,” Ph.D. Thesis, California Institute of Technology, Pasadena, CA.
    • (1990) Ph.D. Thesis, California Institute of Technology
    • Vakakis, A.F.1
  • 25
    • 0000742662 scopus 로고
    • Fundamental and subharmonic resonances in a system with a ‘1-1 internal resonance
    • Vakakis, A. F., 1992a, “Fundamental and subharmonic resonances in a system with a ‘1-1’ internal resonance,” Nonlinear Dynamics, Vol. 3, pp. 123-143.
    • (1992) Nonlinear Dynamics , vol.3 , pp. 123-143
    • Vakakis, A.F.1
  • 26
    • 0026938396 scopus 로고
    • Nonsimilar normal oscillations in a strongly nonlinear discrete system
    • Vakakis, A. F., 1992b, “Nonsimilar normal oscillations in a strongly nonlinear discrete system,” Journal of Sound and Vibration, Vol. 151, No. 22, pp. 341-361.
    • (1992) Journal of Sound and Vibration , vol.151 , Issue.22 , pp. 341-361
    • Vakakis, A.F.1
  • 27
    • 0000472377 scopus 로고
    • A Theorem on the Exact Nonsimilar Steady-State Motions of a Nonlinear Oscillator
    • Vakakis, A. F., and Caughey, T. K., 1992, “A Theorem on the Exact Nonsimilar Steady-State Motions of a Nonlinear Oscillator,” ASME Journal of Applied Mechanics, Vol. 59, pp. 418-424.
    • (1992) ASME Journal of Applied Mechanics , vol.59 , pp. 418-424
    • Vakakis, A.F.1    Caughey, T.K.2
  • 29
    • 0001459972 scopus 로고
    • Normal modes of nonlinear hamiltonian systems
    • Weinstein, A., 1973, “Normal modes of nonlinear hamiltonian systems,” In-ventiones math., Vol. 20, pp. 47-57.
    • (1973) In-Ventiones Math , vol.20 , pp. 47-57
    • Weinstein, A.1


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