메뉴 건너뛰기




Volumn 42, Issue 11-12, 2005, Pages 3339-3373

Non-linear vibrations of free-edge thin spherical shells: Modal interaction rules and 1:1:2 internal resonance

Author keywords

Geometrical non linearities; Internal resonances; Non linear vibrations; Shallow spherical shells

Indexed keywords

ALGEBRA; APPROXIMATION THEORY; DEFLECTION (STRUCTURES); EIGENVALUES AND EIGENFUNCTIONS; ENERGY TRANSFER; GALERKIN METHODS; MATHEMATICAL MODELS; MODAL ANALYSIS; NATURAL FREQUENCIES; PARTIAL DIFFERENTIAL EQUATIONS; RESONANCE; RUNGE KUTTA METHODS; SHELLS (STRUCTURES);

EID: 13444303912     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2004.10.028     Document Type: Article
Times cited : (88)

References (59)
  • 2
    • 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
    • M. Amabili, and M.P. Païdoussis Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction ASME Appl. Mech. Rev. 56 4 2003 349 381
    • (2003) ASME Appl. Mech. Rev. , vol.56 , Issue.4 , pp. 349-381
    • Amabili, M.1    Païdoussis, M.P.2
  • 3
    • 0001413860 scopus 로고    scopus 로고
    • Nonlinear vibrations of simply supported circular cylindrical shells, coupled to quiescent fluid
    • M. Amabili, R. Pellicano, and M.P. PaÏdoussis Nonlinear vibrations of simply supported circular cylindrical shells, coupled to quiescent fluid J. Fluids Struct. 12 1998 883 918
    • (1998) J. Fluids Struct. , vol.12 , pp. 883-918
    • Amabili, M.1    Pellicano, R.2    Païdoussis, M.P.3
  • 4
    • 0000893169 scopus 로고    scopus 로고
    • Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid, part II: Large-amplitude vibrations without flow
    • M. Amabili, F. Pellicano, and M.P. PaÏdoussis Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid, part II: large-amplitude vibrations without flow J. Sound Vib. 228 5 1999 1103 1124
    • (1999) J. Sound Vib. , vol.228 , Issue.5 , pp. 1103-1124
    • Amabili, M.1    Pellicano, F.2    Païdoussis, M.P.3
  • 5
    • 0002470245 scopus 로고    scopus 로고
    • Nonlinear vibrations and multiple resonances of fluid-filled, circular shells, part 1: Equations of motion and numerical results
    • M. Amabili, F. Pellicano, and A.F. Vakakis Nonlinear vibrations and multiple resonances of fluid-filled, circular shells, part 1: equations of motion and numerical results ASME J. Vib. Acoust. 122 2000 346 354
    • (2000) ASME J. Vib. Acoust. , vol.122 , pp. 346-354
    • Amabili, M.1    Pellicano, F.2    Vakakis, A.F.3
  • 6
    • 0000242430 scopus 로고
    • Non-linear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonance conditions
    • F. Benedettini, G. Rega, and R. Alaggio Non-linear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonance conditions J. Sound Vib. 182 5 1995 775 798
    • (1995) J. Sound Vib. , vol.182 , Issue.5 , pp. 775-798
    • Benedettini, F.1    Rega, G.2    Alaggio, R.3
  • 8
    • 0035465970 scopus 로고    scopus 로고
    • A second-order approximation of multi-modal interactions in externally excited circular cylindrical shells
    • C.-M. Chin, and A.H. Nayfeh A second-order approximation of multi-modal interactions in externally excited circular cylindrical shells Nonlinear Dynam. 26 2001 45 66
    • (2001) Nonlinear Dynam. , vol.26 , pp. 45-66
    • Chin, C.-M.1    Nayfeh, A.H.2
  • 9
    • 85143679579 scopus 로고
    • Influence of large amplitudes on free flexural vibrations of rectangular elastic plates
    • H.-N. Chu, and G. Herrmann Influence of large amplitudes on free flexural vibrations of rectangular elastic plates J. Appl. Mech. 23 1956 532 540
    • (1956) J. Appl. Mech. , vol.23 , pp. 532-540
    • Chu, H.-N.1    Herrmann, G.2
  • 10
    • 85148696081 scopus 로고
    • A new theory for the buckling of thin cylinders under axial compression and bending
    • L.H. Donnell A new theory for the buckling of thin cylinders under axial compression and bending Trans. Am. Soc. Mech. Eng. 56 1934 795 806
    • (1934) Trans. Am. Soc. Mech. Eng. , vol.56 , pp. 795-806
    • Donnell, L.H.1
  • 11
    • 0015068034 scopus 로고
    • A new approach to the large-deflction vibrations of imperfect circular disks using Galerkin's procedure
    • G.J. Efstathiades A new approach to the large-deflction vibrations of imperfect circular disks using Galerkin's procedure J. Sound Vib. 16 2 1971 231 253
    • (1971) J. Sound Vib. , vol.16 , Issue.2 , pp. 231-253
    • Efstathiades, G.J.1
  • 12
    • 4644299874 scopus 로고
    • Some studies on the nonlinear dynamic response of shell-type structures
    • oct NASA Langley Research Center
    • Evensen, D.A., Fulton, R.E., oct 1965. Some studies on the nonlinear dynamic response of shell-type structures. Tech. Rep. TMX 56843, NASA Langley Research Center
    • (1965) Tech. Rep. TMX 56843
    • Evensen, D.A.1    Fulton, R.E.2
  • 13
    • 85007679660 scopus 로고
    • Dynamic response and stability of shallow spherical shells subject to time-dependant loading
    • H.A. Evensen, and R.M. Evan-Iwanowsky Dynamic response and stability of shallow spherical shells subject to time-dependant loading AIAA J. 5 5 1967 969 976
    • (1967) AIAA J. , vol.5 , Issue.5 , pp. 969-976
    • Evensen, H.A.1    Evan-Iwanowsky, R.M.2
  • 14
    • 0028767516 scopus 로고
    • Axisymmetric vibrations of imperfect shallow spherical caps under pressure loading
    • P.B. Gonçalves Axisymmetric vibrations of imperfect shallow spherical caps under pressure loading J. Sound Vib. 174 2 1994 249 260
    • (1994) J. Sound Vib. , vol.174 , Issue.2 , pp. 249-260
    • Gonçalves, P.B.1
  • 15
    • 85024563754 scopus 로고
    • Nonlinear vibrations of shallow spherical shells
    • P.L. Grossman, B. Koplik, and Y.-Y. Yu Nonlinear vibrations of shallow spherical shells ASME J. Appl. Mech 39E 1969 451 458
    • (1969) ASME J. Appl. Mech , vol.39 , pp. 451-458
    • Grossman, P.L.1    Koplik, B.2    Yu, Y.-Y.3
  • 17
    • 0003841625 scopus 로고
    • Dstool: A dynamical system toolkit with an interactive graphical interface
    • Center for Applied Mathematics, Cornell University
    • Guckenheimer, J., Myers, M., Wicklin, F., Worfolk, P., 1995. Dstool: a dynamical system toolkit with an interactive graphical interface. Technical Report, Center for Applied Mathematics, Cornell University
    • (1995) Technical Report
    • Guckenheimer, J.1    Myers, M.2    Wicklin, F.3    Worfolk, P.4
  • 18
    • 0021758228 scopus 로고
    • Theoretical and experimental study of modal interaction in a two-degree-of-freedom structure
    • A.G. Haddow, A.D.S. Barr, and D.T. Mook Theoretical and experimental study of modal interaction in a two-degree-of-freedom structure J. Sound Vib. 97 1984 451 473
    • (1984) J. Sound Vib. , vol.97 , pp. 451-473
    • Haddow, A.G.1    Barr, A.D.S.2    Mook, D.T.3
  • 19
    • 13444277032 scopus 로고    scopus 로고
    • Classification of thin shell models deduced from the nonlinear three-dimensional elasticity, part I: The shallow shells
    • A. Hamdouni, and O. Millet Classification of thin shell models deduced from the nonlinear three-dimensional elasticity, part I: the shallow shells Arch. Mech. 55 2 2003 135 175
    • (2003) Arch. Mech. , vol.55 , Issue.2 , pp. 135-175
    • Hamdouni, A.1    Millet, O.2
  • 20
    • 0020890007 scopus 로고
    • Large-amplitude vibrations of geometrically imperfect shallow spherical shells with structural damping
    • D. Hui Large-amplitude vibrations of geometrically imperfect shallow spherical shells with structural damping AIAA J. 21 12 1983 1736 1741
    • (1983) AIAA J. , vol.21 , Issue.12 , pp. 1736-1741
    • Hui, D.1
  • 21
    • 0004311488 scopus 로고
    • On transverse vibrations of shallow spherical shells
    • M.W. Johnson, and E. Reissner On transverse vibrations of shallow spherical shells Quart. Appl. Math. 15 4 1956 367 380
    • (1956) Quart. Appl. Math. , vol.15 , Issue.4 , pp. 367-380
    • Johnson, M.W.1    Reissner, E.2
  • 22
    • 0002630854 scopus 로고
    • Effect of bending on vibrations of spherical shells
    • A. Kalnins Effect of bending on vibrations of spherical shells J. Acoust. Soc. Am. 36 1 1964 74 81
    • (1964) J. Acoust. Soc. Am. , vol.36 , Issue.1 , pp. 74-81
    • Kalnins, A.1
  • 23
    • 0000782640 scopus 로고
    • On the nonlinear theory of thin elastic shells, part I, II and III
    • W.T. Koiter On the nonlinear theory of thin elastic shells, part I, II and III Proc. Kon. Neth. Akad. Wet. B69 1965 1 54
    • (1965) Proc. Kon. Neth. Akad. Wet. , vol.69 , pp. 1-54
    • Koiter, W.T.1
  • 24
    • 0037411955 scopus 로고    scopus 로고
    • Resonant non-linear normal modes, part I: Analytical treatment for structural one-dimensional systems
    • W. Lacarbonara, G. Rega, and A.H. Nayfeh Resonant non-linear normal modes, part I: analytical treatment for structural one-dimensional systems Int. J. Non-Linear Mech. 38 2003 851 872
    • (2003) Int. J. Non-Linear Mech. , vol.38 , pp. 851-872
    • Lacarbonara, W.1    Rega, G.2    Nayfeh, A.H.3
  • 25
    • 0345689697 scopus 로고    scopus 로고
    • The effect of the number of nodal diameters on non-linear interactions in two asymmetric vibration modes of a circular plate
    • W.K. Lee, M.H. Yeo, and S.B. Samoilenko The effect of the number of nodal diameters on non-linear interactions in two asymmetric vibration modes of a circular plate J. Sound. Vib 268 5 2003 1013 1023
    • (2003) J. Sound. Vib , vol.268 , Issue.5 , pp. 1013-1023
    • Lee, W.K.1    Yeo, M.H.2    Samoilenko, S.B.3
  • 26
    • 0003758712 scopus 로고
    • Acoustical Society of America (original issued NASA SP-160, 1969)
    • Leissa, A.W., 1993a. Vibration of plates. Acoustical Society of America (original issued NASA SP-160, 1969)
    • (1993) Vibration of Plates
    • Leissa, A.W.1
  • 27
    • 85040266580 scopus 로고
    • Acoustical Society of America (original issued NASA SP-288, 1973)
    • Leissa, A.W., 1993b. Vibration of shells. Acoustical Society of America (original issued NASA SP-288, 1973)
    • (1993) Vibration of Shells
    • Leissa, A.W.1
  • 28
    • 0000295843 scopus 로고
    • Curvature effects on shallow shell vibrations
    • A.W. Leissa, and A.S. Kadi Curvature effects on shallow shell vibrations J. Sound. Vib. 16 2 1971 173 187
    • (1971) J. Sound. Vib. , vol.16 , Issue.2 , pp. 173-187
    • Leissa, A.W.1    Kadi, A.S.2
  • 29
    • 0017369713 scopus 로고
    • Non-linear analysis of vibrations of irregular plates
    • D.W. Lobitz, A.H. Nayfeh, and D.T. Mook Non-linear analysis of vibrations of irregular plates J. Sound. Vib. 50 2 1977 203 217
    • (1977) J. Sound. Vib. , vol.50 , Issue.2 , pp. 203-217
    • Lobitz, D.W.1    Nayfeh, A.H.2    Mook, D.T.3
  • 31
    • 0012212486 scopus 로고
    • Resonantly forced motion of two quadratically coupled oscillators
    • J.W. Miles Resonantly forced motion of two quadratically coupled oscillators Physica D 13 1984 247 260
    • (1984) Physica D , vol.13 , pp. 247-260
    • Miles, J.W.1
  • 33
    • 0037411923 scopus 로고    scopus 로고
    • Non-linear vibrations of shell-type structures: A review with bibliography
    • F. Moussaoui, and R. Benamar Non-linear vibrations of shell-type structures: a review with bibliography J. Sound. Vib. 255 1 2002 161 184
    • (2002) J. Sound. Vib. , vol.255 , Issue.1 , pp. 161-184
    • Moussaoui, F.1    Benamar, R.2
  • 35
    • 0003686037 scopus 로고    scopus 로고
    • Nonlinear interactions: Analytical, computational and experimental methods
    • New York
    • Nayfeh, A.H., 2000. Nonlinear interactions: analytical, computational and experimental methods. In: Wiley Series in Nonlinear Science, New York
    • (2000) Wiley Series in Nonlinear Science
    • Nayfeh, A.H.1
  • 36
    • 85024523123 scopus 로고
    • Modal interactions in dynamical and structural systems
    • A.H. Nayfeh, and B. Balachandran Modal interactions in dynamical and structural systems ASME Appl. Mech. Rev. 42 11 1989 175 201
    • (1989) ASME Appl. Mech. Rev. , vol.42 , Issue.11 , pp. 175-201
    • Nayfeh, A.H.1    Balachandran, B.2
  • 38
    • 0000301924 scopus 로고
    • On methods for continuous systems with quadratic and cubic nonlinearities
    • A.H. Nayfeh, J.F. Nayfeh, and D.T. Mook On methods for continuous systems with quadratic and cubic nonlinearities Nonlinear Dynam. 3 1992 145 162
    • (1992) Nonlinear Dynam. , vol.3 , pp. 145-162
    • Nayfeh, A.H.1    Nayfeh, J.F.2    Mook, D.T.3
  • 39
    • 0028197991 scopus 로고
    • On nonlinear modes of continuous systems
    • A.H. Nayfeh, and S.A. Nayfeh On nonlinear modes of continuous systems J. Vib. Acoust. 116 1994 129 136
    • (1994) J. Vib. Acoust. , vol.116 , pp. 129-136
    • Nayfeh, A.H.1    Nayfeh, S.A.2
  • 40
    • 0023591610 scopus 로고
    • Non-linear oscillations of circular cylindrical shells
    • A.H. Nayfeh, and R.A. Raouf Non-linear oscillations of circular cylindrical shells Int. J. Solids Struct. 23 12 1987 1625 1638
    • (1987) Int. J. Solids Struct. , vol.23 , Issue.12 , pp. 1625-1638
    • Nayfeh, A.H.1    Raouf, R.A.2
  • 41
    • 0024069822 scopus 로고
    • Experimental observation of amplitude and phase-modulated responses of two internally coupled oscillators to a harmonic excitation
    • A.H. Nayfeh, and L.D. Zavodney Experimental observation of amplitude and phase-modulated responses of two internally coupled oscillators to a harmonic excitation ASME J. Appl. Mech. 55 1988 706 710
    • (1988) ASME J. Appl. Mech. , vol.55 , pp. 706-710
    • Nayfeh, A.H.1    Zavodney, L.D.2
  • 42
    • 0002470239 scopus 로고    scopus 로고
    • Nonlinear vibrations and multiple resonances of fluid-filled, circular shells, part 2: Perturbation analysis
    • F. Pellicano, M. Amabili, and A.F. Vakakis Nonlinear vibrations and multiple resonances of fluid-filled, circular shells, part 2: perturbation analysis ASME J. Vib. Acoust. 122 2000 355 364
    • (2000) ASME J. Vib. Acoust. , vol.122 , pp. 355-364
    • Pellicano, F.1    Amabili, M.2    Vakakis, A.F.3
  • 43
    • 1342283018 scopus 로고    scopus 로고
    • Recent research advances in the dynamic behavior of shells: 1989-2000, part 2: Homogeneous shells
    • M.S. Qatu Recent research advances in the dynamic behavior of shells: 1989-2000, part 2: homogeneous shells ASME Appl. Mech. Rev. 55 5 2002 415 434
    • (2002) ASME Appl. Mech. Rev. , vol.55 , Issue.5 , pp. 415-434
    • Qatu, M.S.1
  • 44
    • 0035285412 scopus 로고    scopus 로고
    • Effects of imperfection on the non-linear oscillations of circular plates spinning near critical speed
    • A. Raman, and C.D. Mote Jr. Effects of imperfection on the non-linear oscillations of circular plates spinning near critical speed Int. J. Non-linear Mech. 36 2001 261 289
    • (2001) Int. J. Non-linear Mech. , vol.36 , pp. 261-289
    • Raman, A.1    Mote Jr., C.D.2
  • 45
    • 0002267471 scopus 로고    scopus 로고
    • Auto-parametric resonance in cylindrical shells using geometric averaging
    • F.M. Robie, A.A. Popov, and J. Thompson Auto-parametric resonance in cylindrical shells using geometric averaging J. Sound Vib. 227 1 1999 65 84
    • (1999) J. Sound Vib. , vol.227 , Issue.1 , pp. 65-84
    • Robie, F.M.1    Popov, A.A.2    Thompson, J.3
  • 47
    • 0016846224 scopus 로고
    • Non-linear resonances in the forced responses of plates, part I: Symmetric responses of circular plates
    • S. Sridhar, D.T. Mook, and A.H. Nayfeh Non-linear resonances in the forced responses of plates, part I: symmetric responses of circular plates J. Sound Vib. 41 3 1975 359 373
    • (1975) J. Sound Vib. , vol.41 , Issue.3 , pp. 359-373
    • Sridhar, S.1    Mook, D.T.2    Nayfeh, A.H.3
  • 48
    • 0017985205 scopus 로고
    • Non-linear resonances in the forced responses of plates, part II: Asymmetric responses of circular plates
    • S. Sridhar, D.T. Mook, and A.H. Nayfeh Non-linear resonances in the forced responses of plates, part II: asymmetric responses of circular plates J. Sound Vib. 59 2 1978 159 170
    • (1978) J. Sound Vib. , vol.59 , Issue.2 , pp. 159-170
    • Sridhar, S.1    Mook, D.T.2    Nayfeh, A.H.3
  • 50
    • 0028426617 scopus 로고
    • Non-linear dynamics of as shallow arch under periodic excitation, I: 1:2 internal resonance
    • W.M. Tien, N.S. Namachchivaya, and A.K. Bajaj Non-linear dynamics of as shallow arch under periodic excitation, I: 1:2 internal resonance Int. J. Nonlinear Mech. 29 3 1994 349 366
    • (1994) Int. J. Nonlinear Mech. , vol.29 , Issue.3 , pp. 349-366
    • Tien, W.M.1    Namachchivaya, N.S.2    Bajaj, A.K.3
  • 51
    • 0000120220 scopus 로고
    • The influence of dynamical imperfection on the vibration of rotating disks
    • S.A. Tobias, and R.N. Arnold The influence of dynamical imperfection on the vibration of rotating disks Proc. of the Instn. of Mech. Eng. 171 1957 669 690
    • (1957) Proc. of the Instn. of Mech. Eng. , vol.171 , pp. 669-690
    • Tobias, S.A.1    Arnold, R.N.2
  • 53
    • 0042816749 scopus 로고    scopus 로고
    • Asymmetric non-linear forced vibrations of free-edge circular plates, part 1: Theory
    • C. Touzé, O. Thomas, and A. Chaigne Asymmetric non-linear forced vibrations of free-edge circular plates, part 1: theory J. Sound. Vib. 258 4 2002 649 676
    • (2002) J. Sound. Vib. , vol.258 , Issue.4 , pp. 649-676
    • Touzé, C.1    Thomas, O.2    Chaigne, A.3
  • 54
    • 2342517458 scopus 로고    scopus 로고
    • Hardening/softening behaviour in nonlinear oscillations of structural systems using non-linear normal modes
    • C. Touzé, O. Thomas, and A. Chaigne Hardening/softening behaviour in nonlinear oscillations of structural systems using non-linear normal modes J. Sound. Vib. 273 1-2 2004 77 101
    • (2004) J. Sound. Vib. , vol.273 , Issue.1-2 , pp. 77-101
    • Touzé, C.1    Thomas, O.2    Chaigne, A.3
  • 56
    • 0017456454 scopus 로고
    • On the internal resonance in a non-linear two-degree-of-freedom system
    • T. Yamamoto, and K. Yasuda On the internal resonance in a non-linear two-degree-of-freedom system Bull. Jpn. Soc. Mech. Eng. 20 1977 168 175
    • (1977) Bull. Jpn. Soc. Mech. Eng. , vol.20 , pp. 168-175
    • Yamamoto, T.1    Yasuda, K.2
  • 57
    • 0021506190 scopus 로고
    • Nonlinear forced oscillations of a shallow spherical shell
    • K. Yasuda, and G. Kushida Nonlinear forced oscillations of a shallow spherical shell Bull. JSME 27 232 1984 2233 2240
    • (1984) Bull. JSME , vol.27 , Issue.232 , pp. 2233-2240
    • Yasuda, K.1    Kushida, G.2
  • 58
    • 0002857818 scopus 로고    scopus 로고
    • The non-linear vibration and dynamic instability of thin shallow shells
    • Z.M. Ye The non-linear vibration and dynamic instability of thin shallow shells J. Sound Vib. 202 3 1997 303 311
    • (1997) J. Sound Vib. , vol.202 , Issue.3 , pp. 303-311
    • Ye, Z.M.1
  • 59
    • 0037206996 scopus 로고    scopus 로고
    • Corrected solvability conditions for non-linear asymmetric vibrations of a circular plate
    • M.H. Yeo, and W.K. Lee Corrected solvability conditions for non-linear asymmetric vibrations of a circular plate J. Sound. Vib 257 4 2002 653 665
    • (2002) J. Sound. Vib , vol.257 , Issue.4 , pp. 653-665
    • Yeo, M.H.1    Lee, W.K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.