Internal resonances in non-linear vibrations of a laminated circular cylindrical shell

Nonlinear Dynamics

Volumn 69, Issue 3, 2012, Pages 755-770

  Amabili, Marco ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Circular cylindrical shells; Forced vibrations; Internal resonances; Laminated composite; Non linear vibrations; Rotary inertia; Shear deformation; Shells

Indexed keywords

CIRCULAR CYLINDRICAL SHELLS; FORCED VIBRATION; INTERNAL RESONANCE; NON-LINEAR VIBRATIONS; ROTARY INERTIAS; SHELLS;

BIFURCATION (MATHEMATICS); CYLINDERS (SHAPES); EQUATIONS OF MOTION; LAMINATED COMPOSITES; LAMINATING; SHEAR DEFORMATION; SHELLS (STRUCTURES);

RESONANCE;

EID: 84863989938     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-011-0302-1     Document Type: Article

References (26)

1. Amabili, M., Pellicano, F., Vakakis, A.F.: Nonlinear vibrations and multiple resonances of fluid-filled, circular shells, Part I: Equations of motion and numerical results. ASME J. Vib. Acoust. 122, 346-354 (2000)
2. Pellicano, F., Amabili, M., Vakakis, A.F.: Nonlinear vibrations and multiple resonances of fluid-filled, circular shells, Part II: Perturbation analysis. ASME J. Vib. Acoust. 122, 355-364 (2000)
3. Iu, V.P., Chia, C.Y.: Effect of transverse shear on nonlinear vibration and postbuckling of anti-symmetric cross-ply imperfect cylindrical shells. Int. J. Mech. Sci. 30, 705-718 (1988)
4. Iu, V.P., Chia, C.Y.: Non-linear vibration and postbuckling of unsymmetric cross-ply circular cylindrical shells. Int. J. Solids Struct. 24, 195-210 (1988) (Pubitemid 18580507)
5. Fu, Y.M., Chia, C.Y.: Non-linear vibration and postbuckling of generally laminated circular cylindrical thick shells with non-uniform boundary conditions. Int. J. Non-Linear Mech. 28, 313-327 (1993)
6. Ganapathi, M., Varadan, T.K.: Application of a fieldconsistent shear flexible element for nonlinear dynamic analysis of laminated shells. Finite Elem. Anal. Des. 12, 105-116 (1992) (Pubitemid 23570436)
7. Ganapathi, M., Varadan, T.K.: Nonlinear free flexural vibrations of laminated circular cylindrical shells. Compos. Struct. 30, 33-49 (1995)
8. Lakis, A.A., Selmane, A., Toledano, A.: Non-linear free vibration analysis of laminated orthotropic cylindrical shells. Int. J. Mech. Sci. 40, 27-49 (1998) (Pubitemid 128393326)
9. Toorani, M.H.: Dynamics of the geometrically non-linear analysis of anisotropic laminated cylindrical shells. Int. J. Non-Linear Mech. 38, 1315-1335 (2003)
10. Nayfeh, J.F., Rivieccio, N.J.: Nonlinear vibration of composite shell subjected to resonant excitations. J. Aerosp. Eng. 13, 59-68 (2000)
11. Jansen, E.L.: The effect of static loading and imperfections on the nonlinear vibrations of laminated cylindrical shells. J. Sound Vib. 315, 1035-1046 (2008)
12. Jansen, E.L.: A perturbation method for nonlinear vibrations of imperfect structures: Application to cylindrical shell vibrations. Int. J. Solids Struct. 45, 1124-1145 (2008) (Pubitemid 350088766)
13. Jansen, E.L.: Effect of boundary conditions on nonlinear vibration and flutter of laminated cylindrical shells. ASME J. Vib. Acoust. 130, 011003 (2008)
14. Amabili, M.: Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories. Compos. Struct. 94, 207-220 (2011). doi:10.1016/j. compstruct.2011.07.001
15. Amabili, M., Reddy, J.N.: A new non-linear higher-order shear deformation theory for large-Amplitude vibrations of laminated doubly curved shells. Int. J. Non-Linear Mech. 45, 409-418 (2010)
16. Ribeiro, P.: On the influence of membrane inertia and shear deformation on the geometrically non-linear vibrations of open, cylindrical, laminated clamped shells. Compos. Sci. Technol. 69, 176-185 (2009)
17. Amabili, M.: Nonlinear Vibrations and Stability of Shells and Plates. Cambridge University Press, New York (2008)
18. Reddy, J.N., Liu, C.F.: A higher-order shear deformation theory of laminated elastic shells. Int. J. Eng. Sci. 23, 319-330 (1985) (Pubitemid 15494942)
19. Carrera, E., Brischetto, S., Cinefra, M., Soave, M.: Effects of thickness stretching in functionally graded plates and shells. Compos., Part B 42, 123-133 (2011)
20. Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C.: Analysis of laminated doubly-curved shells by a layerwise theory and radial basis functions collocation, accounting for through-The-Thickness deformations. Comput. Mech. 48, 13-25 (2011)
21. Ashton, J.E., Whitney, J.M.: Theory of Laminated Plates. Technomic, Stamford (1970)
22. Nayak, A.K., Moy, S.S.J., Shenoi, R.A.: Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory. Compos., Part B 33, 505-519 (2002) (Pubitemid 35152334)
23. Amabili, M.: Comparison of shell theories for largeamplitude vibrations of circular cylindrical shells: Lagrangian approach. J. Sound Vib. 264, 1091-1125 (2003)
24. Messina, A., Soldatos, K.P.: Ritz-Type dynamic analysis of cross-ply laminated circular cylinders subjected to different boundary conditions. J. Sound Vib. 227, 749-768 (1999) (Pubitemid 129531607)
25. Matsunaga, H.: Vibration and buckling of cross-ply laminated composite circular cylindrical shells according to a global higher-order theory. Int. J. Mech. Sci. 49, 1060-1075 (2007) (Pubitemid 46963255)
26. Doedel, E.J., Champneys, A.R., Fairgrieve, T.F., Kuznetsov, Y.A., Sandstede, B., Wang, X.: AUTO 97: Continuation and bifurcation software for ordinary differential equations (with HomCont). Concordia University, Montreal, Canada (1998)