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Volumn 41, Issue 5, 2006, Pages 678-692

Non-linear behaviour of free-edge shallow spherical shells: Effect of the geometry

Author keywords

Hardening softening behaviour; Internal resonance; Non linear normal modes; Shallow spherical shells

Indexed keywords

COMPUTATION THEORY; GEOMETRY; HARDENING; MOTION CONTROL; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33745891539     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2005.12.004     Document Type: Article
Times cited : (37)

References (49)
  • 1
    • 0022349593 scopus 로고
    • Non-linear frequency shifts in quasispherical-cap shells: pitch glide in Chinese gongs
    • Fletcher N.H. Non-linear frequency shifts in quasispherical-cap shells: pitch glide in Chinese gongs. J. Acoust. Soc. Am. 78 6 (1985) 2069-2071
    • (1985) J. Acoust. Soc. Am. , vol.78 , Issue.6 , pp. 2069-2071
    • Fletcher, N.H.1
  • 2
    • 0039252495 scopus 로고    scopus 로고
    • Lyapunov exponents from experimental time series: application to cymbal vibrations
    • Touzé C., and Chaigne A. Lyapunov exponents from experimental time series: application to cymbal vibrations. Acta Acustica 86 3 (2000) 557-567
    • (2000) Acta Acustica , vol.86 , Issue.3 , pp. 557-567
    • Touzé, C.1    Chaigne, A.2
  • 4
    • 0000120219 scopus 로고
    • Free undamped non-linear vibrations of imperfect circular disks
    • Tobias S.A. Free undamped non-linear vibrations of imperfect circular disks. Proc. Inst. Mech. Eng. 171 (1957) 691-700
    • (1957) Proc. Inst. Mech. Eng. , vol.171 , pp. 691-700
    • Tobias, S.A.1
  • 5
    • 84982354062 scopus 로고
    • Influence of large amplitudes on flexural vibrations of elastic plates
    • Yamaki N. Influence of large amplitudes on flexural vibrations of elastic plates. Zur Angew. Math. Mech. 41 12 (1961) 501-510
    • (1961) Zur Angew. Math. Mech. , vol.41 , Issue.12 , pp. 501-510
    • Yamaki, N.1
  • 6
    • 0015631048 scopus 로고
    • On the modal equations of large amplitude flexural vibration of beams, plates, rings and shells
    • Pandalai K.A.V., and Sathyamoorthy M. On the modal equations of large amplitude flexural vibration of beams, plates, rings and shells. Int. J. Non-linear Mech. 3 (1973) 213-218
    • (1973) Int. J. Non-linear Mech. , vol.3 , pp. 213-218
    • Pandalai, K.A.V.1    Sathyamoorthy, M.2
  • 7
    • 0016846224 scopus 로고
    • Non-linear resonances in the forced responses of plates, Part I: symmetric responses of circular plates
    • Sridhar S., Mook D.T., and Nayfeh A.H. 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
  • 8
    • 0042816749 scopus 로고    scopus 로고
    • Asymmetric non-linear forced vibrations of free-edge circular plates, Part I: theory
    • Touzé C., Thomas O., and Chaigne A. Asymmetric non-linear forced vibrations of free-edge circular plates, Part I: 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
  • 9
    • 0042383082 scopus 로고    scopus 로고
    • Asymmetric non-linear forced vibrations of free-edge circular plates, Part II: experiments
    • Thomas O., Touzé C., and Chaigne A. Asymmetric non-linear forced vibrations of free-edge circular plates, Part II: experiments. J. Sound Vib. 265 5 (2003) 1075-1101
    • (2003) J. Sound Vib. , vol.265 , Issue.5 , pp. 1075-1101
    • Thomas, O.1    Touzé, C.2    Chaigne, A.3
  • 10
    • 0018263451 scopus 로고
    • The role of median surface curvature in large amplitude flexural vibrations of thin shells
    • Prathap G., and Pandalai K.A.V. The role of median surface curvature in large amplitude flexural vibrations of thin shells. J. Sound Vib. 60 1 (1978) 119-131
    • (1978) J. Sound Vib. , vol.60 , Issue.1 , pp. 119-131
    • Prathap, G.1    Pandalai, K.A.V.2
  • 11
    • 33745918557 scopus 로고    scopus 로고
    • O. Thomas, C. Touzé, A. Chaigne, Non-linear behavior of gongs through the dynamic of simple rods systems, in: Proceedings of the International Symposium on Musical Acoustics, Perugia, Italy, September 2001, pp. 173-178.
  • 12
    • 85007679660 scopus 로고
    • Dynamic response and stability of shallow spherical shells subject to time-dependant loading
    • Evensen H.A., and Evan-Iwanowsky R.M. 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
  • 13
    • 85024563754 scopus 로고
    • Nonlinear vibrations of shallow spherical shells
    • Grossman P.L., Koplik B., and Yu Y.-Y. Nonlinear vibrations of shallow spherical shells. ASME J. Appl. Mech. 39E (1969) 451-458
    • (1969) ASME J. Appl. Mech. , vol.39 E , pp. 451-458
    • Grossman, P.L.1    Koplik, B.2    Yu, Y.-Y.3
  • 14
    • 0021506190 scopus 로고
    • Nonlinear forced oscillations of a shallow spherical shell
    • Yasuda K., and Kushida G. 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
  • 15
    • 0042471254 scopus 로고
    • Large amplitude axisymmetric vibrations of moderately thick spherical caps
    • Singh P.N., Sundarajan V., and Dias Y.C. Large amplitude axisymmetric vibrations of moderately thick spherical caps. J. Sound Vib. 20 3 (1972) 269-276
    • (1972) J. Sound Vib. , vol.20 , Issue.3 , pp. 269-276
    • Singh, P.N.1    Sundarajan, V.2    Dias, Y.C.3
  • 16
    • 0028416992 scopus 로고
    • Vibrations of moderately thick shallow spherical shells at large amplitude
    • Sathyamoorthy M. Vibrations of moderately thick shallow spherical shells at large amplitude. J. Sound Vib. 172 1 (1994) 63-70
    • (1994) J. Sound Vib. , vol.172 , Issue.1 , pp. 63-70
    • Sathyamoorthy, M.1
  • 17
    • 0018026725 scopus 로고
    • Non-linear flexural oscillations of orthotropic shallow spherical shells
    • Varadan T.K., and Pandalai K.A.V. Non-linear flexural oscillations of orthotropic shallow spherical shells. Comput. Struct. 9 (1978) 417-425
    • (1978) Comput. Struct. , vol.9 , pp. 417-425
    • Varadan, T.K.1    Pandalai, K.A.V.2
  • 18
    • 0027798785 scopus 로고
    • A time-mode approach to non-linear vibrations of orthotropic thin shallow spherical shells
    • Li D. A time-mode approach to non-linear vibrations of orthotropic thin shallow spherical shells. Int. J. Solids Struct. 30 22 (1993) 3113-3128
    • (1993) Int. J. Solids Struct. , vol.30 , Issue.22 , pp. 3113-3128
    • Li, D.1
  • 19
    • 0028767516 scopus 로고
    • Axisymmetric vibrations of imperfect shallow spherical caps under pressure loading
    • Gonçalves P.B. 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
  • 20
    • 0020890007 scopus 로고
    • Large-amplitude vibrations of geometrically imperfect shallow spherical shells with structural damping
    • Hui D. 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
    • 0000295843 scopus 로고
    • Curvature effects on shallow shell vibrations
    • Leissa A.W., and Kadi A.S. 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
  • 22
    • 0031550183 scopus 로고    scopus 로고
    • Large amplitude free vibration behavior of doubly curved shallow open shells with simply supported edges
    • Shin D.K. Large amplitude free vibration behavior of doubly curved shallow open shells with simply supported edges. Comput. Struct. 62 1 (1997) 35-49
    • (1997) Comput. Struct. , vol.62 , Issue.1 , pp. 35-49
    • Shin, D.K.1
  • 23
    • 33745886746 scopus 로고    scopus 로고
    • K.A. Alhazza, Nonlinear vibrations of doubly curved cross-ply shallow shells, Ph.D. Thesis, Virginia Polytechnic Institute and State University, 2002.
  • 24
    • 0031186408 scopus 로고    scopus 로고
    • On the discretization of distributed-parameter systems with quadratic and cubic non-linearities
    • Nayfeh A.H., and Lacarbonara W. On the discretization of distributed-parameter systems with quadratic and cubic non-linearities. Nonlinear Dyn. 13 (1997) 203-220
    • (1997) Nonlinear Dyn. , vol.13 , pp. 203-220
    • Nayfeh, A.H.1    Lacarbonara, W.2
  • 25
    • 13544250560 scopus 로고    scopus 로고
    • Non-linear vibrations of doubly curved shallow shells
    • Amabili M. Non-linear vibrations of doubly curved shallow shells. Int. J. Non-linear Mech. 40 (2005) 683-710
    • (2005) Int. J. Non-linear Mech. , vol.40 , pp. 683-710
    • Amabili, M.1
  • 26
    • 0000301924 scopus 로고
    • On methods for continuous systems with quadratic and cubic nonlinearities
    • Nayfeh A.H., Nayfeh J.F., and Mook D.T. On methods for continuous systems with quadratic and cubic nonlinearities. Nonlinear Dyn. 3 (1992) 145-162
    • (1992) Nonlinear Dyn. , vol.3 , pp. 145-162
    • Nayfeh, A.H.1    Nayfeh, J.F.2    Mook, D.T.3
  • 27
    • 0001413860 scopus 로고    scopus 로고
    • Non-linear vibrations of simply supported, circular cylindrical shells, coupled to quiescent fluid
    • Amabili M., Pellicano F., and Pai{dotless}̈doussis M.P. Non-linear 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, F.2    Païdoussis, M.P.3
  • 28
    • 0000893169 scopus 로고    scopus 로고
    • Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid, Part II: large-amplitude vibrations without flow
    • Amabili M., Pellicano F., and Pai{dotless}̈doussis M.P. 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
  • 29
    • 0036778880 scopus 로고    scopus 로고
    • Effect of the geometry on the non-linear vibration of circular cylindrical shells
    • Pellicano F., Amabili M., and Pai{dotless}̈doussis M.P. Effect of the geometry on the non-linear vibration of circular cylindrical shells. Int. J. Non-linear Mech. 37 (2002) 1181-1198
    • (2002) Int. J. Non-linear Mech. , vol.37 , pp. 1181-1198
    • Pellicano, F.1    Amabili, M.2    Païdoussis, M.P.3
  • 30
    • 0000608731 scopus 로고    scopus 로고
    • Comments on the nonlinear vibrations of cylindrical shells
    • Dowell E.H. Comments on the nonlinear vibrations of cylindrical shells. J. Fluids Struct. 12 8 (1998) 1087-1089
    • (1998) J. Fluids Struct. , vol.12 , Issue.8 , pp. 1087-1089
    • Dowell, E.H.1
  • 31
    • 0013439947 scopus 로고    scopus 로고
    • Further comments on nonlinear vibrations of shells
    • Amabili M., Pellicano F., and Pai{dotless}̈doussis M.P. Further comments on nonlinear vibrations of shells. J. Fluids Struct. 13 1 (1999) 159-160
    • (1999) J. Fluids Struct. , vol.13 , Issue.1 , pp. 159-160
    • Amabili, M.1    Pellicano, F.2    Païdoussis, M.P.3
  • 32
    • 0001169030 scopus 로고    scopus 로고
    • Nonlinear vibrations of cylindrical shells-logical rationale
    • Evensen D.A. Nonlinear vibrations of cylindrical shells-logical rationale. J. Fluids Struct. 13 1 (1999) 161-164
    • (1999) J. Fluids Struct. , vol.13 , Issue.1 , pp. 161-164
    • Evensen, D.A.1
  • 33
    • 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., and Pai{dotless}̈doussis M.P. 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
  • 34
    • 0035284153 scopus 로고    scopus 로고
    • Methods for dimension reduction and their applications in nonlinear dynamics
    • Steindl A., and Troger H. Methods for dimension reduction and their applications in nonlinear dynamics. Int. J. Solids Struct. 38 (2001) 2131-2147
    • (2001) Int. J. Solids Struct. , vol.38 , pp. 2131-2147
    • Steindl, A.1    Troger, H.2
  • 35
    • 0032097205 scopus 로고    scopus 로고
    • Reduced-order models of weakly non-linear spatially continuous systems
    • Nayfeh A.H. Reduced-order models of weakly non-linear spatially continuous systems. Nonlinear Dyn. 16 (1998) 105-125
    • (1998) Nonlinear Dyn. , vol.16 , pp. 105-125
    • Nayfeh, A.H.1
  • 36
    • 33745891127 scopus 로고    scopus 로고
    • W. Lacarbonara, A theoretical and experimental investigation of non-linear vibrations of buckled beams, Ph.D. Thesis, Virginia Polytechnic Institute and State University, 1997.
  • 37
    • 0011646339 scopus 로고    scopus 로고
    • Reduction methods for nonlinear vibrations of spatially continuous systems with initial curvature
    • Rega G., Lacarbonara W., and Nayfeh A.H. Reduction methods for nonlinear vibrations of spatially continuous systems with initial curvature. Solid Mech. Appl. 77 (2000) 235-246
    • (2000) Solid Mech. Appl. , vol.77 , pp. 235-246
    • Rega, G.1    Lacarbonara, W.2    Nayfeh, A.H.3
  • 38
    • 0141595215 scopus 로고    scopus 로고
    • Non-linear responses of suspended cables to primary resonance excitation
    • Arafat H.N., and Nayfeh A.H. Non-linear responses of suspended cables to primary resonance excitation. J. Sound Vib. 266 (2003) 325-354
    • (2003) J. Sound Vib. , vol.266 , pp. 325-354
    • Arafat, H.N.1    Nayfeh, A.H.2
  • 39
    • 0027911991 scopus 로고
    • Normal modes for non-linear vibratory systems
    • Shaw S.W., and Pierre C. Normal modes for non-linear vibratory systems. J. Sound Vib. 164 1 (1993) 85-124
    • (1993) J. Sound Vib. , vol.164 , Issue.1 , pp. 85-124
    • Shaw, S.W.1    Pierre, C.2
  • 40
    • 2342517458 scopus 로고    scopus 로고
    • Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes
    • Touzé C., Thomas O., and Chaigne A. Hardening/softening behaviour in non-linear 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
  • 41
    • 13444303912 scopus 로고    scopus 로고
    • Non-linear vibrations of free-edge thin spherical shells: modal interaction rules and 1:1:2 internal resonance
    • Thomas O., Touzé C., and Chaigne A. Non-linear vibrations of free-edge thin spherical shells: modal interaction rules and 1:1:2 internal resonance. Int. J. Solids Struct. 42 11-12 (2005) 3339-3373
    • (2005) Int. J. Solids Struct. , vol.42 , Issue.11-12 , pp. 3339-3373
    • Thomas, O.1    Touzé, C.2    Chaigne, A.3
  • 42
    • 25144441610 scopus 로고    scopus 로고
    • O. Thomas, E. Luminais, C. Touzé, Non-linear modal interactions in free-edge thin spherical shells: measurements of a 1:1:2 internal resonance, in: Proceedings of the Third MIT Conference on Computational Fluid and Solid Mechanics, Boston, 2005.
  • 45
    • 0001055171 scopus 로고
    • Analytical form of differential equations
    • Brjuno A.D. Analytical form of differential equations. Trans. Moscow Math. Soc. 25 (1971) 131-288
    • (1971) Trans. Moscow Math. Soc. , vol.25 , pp. 131-288
    • Brjuno, A.D.1
  • 46
    • 0026223029 scopus 로고
    • Analysis of non-linear dynamical systems by the normal form theory
    • Jézéquel L., and Lamarque C.H. Analysis of non-linear dynamical systems by the normal form theory. J. Sound Vib. 149 3 (1991) 429-459
    • (1991) J. Sound Vib. , vol.149 , Issue.3 , pp. 429-459
    • Jézéquel, L.1    Lamarque, C.H.2
  • 47
    • 10044269430 scopus 로고    scopus 로고
    • Asymptotic non-linear normal modes for large amplitude vibrations of continuous structures
    • Touzé C., Thomas O., and Huberdeau A. Asymptotic non-linear normal modes for large amplitude vibrations of continuous structures. Comput. Struct. 82 31-32 (2004) 2671-2682
    • (2004) Comput. Struct. , vol.82 , Issue.31-32 , pp. 2671-2682
    • Touzé, C.1    Thomas, O.2    Huberdeau, A.3
  • 49
    • 0002630854 scopus 로고
    • Effect of bending on vibrations of spherical shells
    • Kalnins A. 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


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