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Volumn 82, Issue 31-32, 2004, Pages 2659-2670

The application of Hamiltonian dynamics and averaging to nonlinear shell vibration

Author keywords

1:1:2 Resonance; Auto parametric resonance; Cylindrical shells; Hamiltonian dynamics; Method of averaging; Spherical spring pendulum

Indexed keywords

DEFORMATION; ENERGY TRANSFER; FUNCTIONS; HAMILTONIANS; INTEGRAL EQUATIONS; NONLINEAR SYSTEMS; POTENTIAL ENERGY; RESONANCE; VIBRATION CONTROL;

EID: 10044291597     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2004.03.078     Document Type: Article
Times cited : (9)

References (29)
  • 1
    • 0002267471 scopus 로고    scopus 로고
    • Auto-parametric resonance in cylindrical shells using geometric averaging
    • McRobie FA, Popov AA, Thompson JMT. Auto-parametric resonance in cylindrical shells using geometric averaging. J Sound Vibr 1999;227(1):65-84.
    • (1999) J Sound Vibr , vol.227 , Issue.1 , pp. 65-84
    • McRobie, F.A.1    Popov, A.A.2    Thompson, J.M.T.3
  • 2
    • 0035969433 scopus 로고    scopus 로고
    • Chaotic energy exchange through auto-parametric resonance in cylindrical shells
    • Popov AA, Thompson JMT, McRobie FA. Chaotic energy exchange through auto-parametric resonance in cylindrical shells. J Sound Vibr 2001;248(3):395-411.
    • (2001) J Sound Vibr , vol.248 , Issue.3 , pp. 395-411
    • Popov, A.A.1    Thompson, J.M.T.2    McRobie, F.A.3
  • 3
    • 0347600424 scopus 로고    scopus 로고
    • Auto-parametric resonance in thin cylindrical shells using the slow fluctuation method
    • Popov AA. Auto-parametric resonance in thin cylindrical shells using the slow fluctuation method. Thin-Walled Struct 2004;42(3):475-95.
    • (2004) Thin-Walled Struct , vol.42 , Issue.3 , pp. 475-495
    • Popov, A.A.1
  • 5
    • 0001833786 scopus 로고
    • Nonlinear vibrations of circular cylindrical shells
    • Fung YC, Sechler EE, editors. New Jersey: Prentice-Hall
    • Evensen DA. Nonlinear vibrations of circular cylindrical shells. In: Fung YC, Sechler EE, editors. Thin-shell structures. New Jersey: Prentice-Hall; 1974. p. 133-55.
    • (1974) Thin-shell Structures , pp. 133-155
    • Evensen, D.A.1
  • 6
    • 85024523123 scopus 로고
    • Modal interactions in dynamical and structural systems
    • Nayfeh AH, Balachandran B. Modal interactions in dynamical and structural systems. Appl Mech Rev 1989;42((11)Part 2):S175-201.
    • (1989) Appl Mech Rev , vol.42 , Issue.11 PART 2
    • Nayfeh, A.H.1    Balachandran, B.2
  • 7
    • 4644275965 scopus 로고    scopus 로고
    • Bifurcation and chaos in externally excited circular cylindrical shells
    • Chin CM, Nayfeh AH. Bifurcation and chaos in externally excited circular cylindrical shells. J Appl Mech 1996;63(3): 565-74.
    • (1996) J Appl Mech , vol.63 , Issue.3 , pp. 565-574
    • Chin, C.M.1    Nayfeh, A.H.2
  • 8
    • 0000543533 scopus 로고    scopus 로고
    • Suppression of escape by resonant modal interactions: In shell vibration and heaveroll capsize
    • Thompson JMT, de Souza JR. Suppression of escape by resonant modal interactions: in shell vibration and heaveroll capsize. Proc Roy Soc Lond 1996;A452:2527-50.
    • (1996) Proc Roy Soc Lond , vol.A452 , pp. 2527-2550
    • Thompson, J.M.T.1    De Souza, J.R.2
  • 9
    • 0001706860 scopus 로고    scopus 로고
    • Low dimensional models of shell vibrations. Parametrically excited vibrations of cylindrical shells
    • Popov AA, Thompson JMT, McRobie FA. Low dimensional models of shell vibrations. Parametrically excited vibrations of cylindrical shells. J Sound Vibr 1998;209(1): 163-86.
    • (1998) J Sound Vibr , vol.209 , Issue.1 , pp. 163-186
    • Popov, A.A.1    Thompson, J.M.T.2    McRobie, F.A.3
  • 10
    • 0037411923 scopus 로고    scopus 로고
    • Non-linear vibrations of shelltype structures: A review with bibliography
    • Moussaoui F, Benamar R. Non-linear vibrations of shelltype structures: a review with bibliography. J Sound Vibr 2002;255(1):161-84.
    • (2002) J Sound Vibr , vol.255 , Issue.1 , pp. 161-184
    • Moussaoui, F.1    Benamar, R.2
  • 11
    • 1342283018 scopus 로고    scopus 로고
    • Recent research advances in the dynamic behavior of shells: 1989-2000. Part 2: Homogeneous shells
    • Qatu MS. Recent research advances in the dynamic behavior of shells: 1989-2000. Part 2: Homogeneous shells. Appl Mech Rev 2002;55(5):415-34.
    • (2002) Appl Mech Rev , vol.55 , Issue.5 , pp. 415-434
    • Qatu, M.S.1
  • 12
    • 0037822717 scopus 로고    scopus 로고
    • Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction
    • Amabili M, Paldoussis MP. Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Appl Mech Rev 2003;56(4):349-81.
    • (2003) Appl Mech Rev , vol.56 , Issue.4 , pp. 349-381
    • Amabili, M.1    Paldoussis, M.P.2
  • 15
    • 10044237031 scopus 로고
    • Asymptotic analysis of Hamiltonian systems
    • Verhulst F, editor. Berlin: Springer-Verlag
    • Verhulst F. Asymptotic analysis of Hamiltonian systems. In: Verhulst F, editor. Asymptotic analysis II. Lecture notes in mathematics, vol. 985. Berlin: Springer-Verlag; 1983.
    • (1983) Asymptotic Analysis II. Lecture Notes in Mathematics, Vol. , vol.985
    • Verhulst, F.1
  • 16
    • 0000744221 scopus 로고
    • Discrete symmetric dynamical systems at the main resonances with application to axi-symmetric galaxies
    • Verhulst F. Discrete symmetric dynamical systems at the main resonances with application to axi-symmetric galaxies. Phil Trans Roy Soc Lond 1979;A290:435-65.
    • (1979) Phil Trans Roy Soc Lond , vol.A290 , pp. 435-465
    • Verhulst, F.1
  • 17
    • 0010675629 scopus 로고
    • The 1:2:1-resonance, its periodic orbits and integrals
    • Verhulst F, editor. Berlin: Springer-Verlag
    • van der Aa E, Sanders JA. The 1:2:1-resonance, its periodic orbits and integrals. In: Verhulst F, editor. Asymptotic analysis. Lecture notes in mathematics, vol. 711, Berlin: Springer-Verlag; 1979.
    • (1979) Asymptotic Analysis. Lecture Notes in Mathematics , vol.711
    • Van Der Aa, E.1    Sanders, J.A.2
  • 18
    • 0039181350 scopus 로고
    • First order resonances in three-degrees-of-freedom systems
    • van der Aa E. First order resonances in three-degrees-of-freedom systems. Celest Mech 1983;31:163-91.
    • (1983) Celest Mech , vol.31 , pp. 163-191
    • Van Der Aa, E.1
  • 19
    • 0022888791 scopus 로고
    • Hidden symmetry concepts in the elastic buckling of axially-loaded cylinders
    • Hunt GW, Williams KAJ, Cowell RO. Hidden symmetry concepts in the elastic buckling of axially-loaded cylinders. Int J Solids Struct 1986;22:1501-15.
    • (1986) Int J Solids Struct , vol.22 , pp. 1501-1515
    • Hunt, G.W.1    Williams, K.A.J.2    Cowell, R.O.3
  • 21
    • 44649112263 scopus 로고
    • Modal equations for the nonlinear flexural vibrations of a cylindrical shell
    • Revised and corrected in cooperation with Tang D, Duke University School of Engineering Report 98-1, 1998
    • Dowell EH, Ventres CS. Modal equations for the nonlinear flexural vibrations of a cylindrical shell. Int J Solids Struct 1968;4:975-91. Revised and corrected in cooperation with Tang D, Duke University School of Engineering Report 98-1, 1998.
    • (1968) Int J Solids Struct , vol.4 , pp. 975-991
    • Dowell, E.H.1    Ventres, C.S.2
  • 22
    • 18244377342 scopus 로고
    • Classical mechanics
    • Addison-Wesley
    • Goldstein H. Classical mechanics. Reading, Mass.: Addison-Wesley; 1980.
    • (1980) Reading, Mass.
    • Goldstein, H.1
  • 26
    • 0012097571 scopus 로고
    • A universal instability of many-dimensional oscillator systems
    • Chirikov BV. A universal instability of many-dimensional oscillator systems. Phys Rep 1979;52:263-379.
    • (1979) Phys Rep , vol.52 , pp. 263-379
    • Chirikov, B.V.1
  • 27
    • 0002018756 scopus 로고
    • Non-integrability of the 1:1:2-resonance
    • Duistermaat JJ. Non-integrability of the 1:1:2-resonance. Ergod Th Dyn Syst 1984;4:553-68.
    • (1984) Ergod Th Dyn Syst , vol.4 , pp. 553-568
    • Duistermaat, J.J.1
  • 29
    • 0034851383 scopus 로고    scopus 로고
    • Symmetry and resonance in Hamiltonian systems
    • Tuwankotta JM, Verhulst F. Symmetry and resonance in Hamiltonian systems. SIAM J Appl Math 2000;61(4): 1369-85.
    • (2000) SIAM J Appl Math , vol.61 , Issue.4 , pp. 1369-1385
    • Tuwankotta, J.M.1    Verhulst, F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.