Influence of Modal Coupling on the Nonlinear Vibration of Simply Supported Cylindrical Panels

Abstract:

The aim of this paper is to analyse the influence of the nonlinear modal coupling on the nonlinear vibrations of a simply supported cylindrical panel excited by a time dependent transversal load. The cylindrical panel is modeled by the Donnell nonlinear shallow shell theory and the lateral displacement field is based on a perturbation procedure. The axial and circumferential displacement are described in terms of the obtained lateral displacement, generating a precise low-dimensional model that satisfies all transversal boundary conditions. The discretized equations of motion in time domain are determined by applying the standard Galerkin method. Various numerical techniques are employed to obtain the cylindrical panel resonance curves, bifurcation scenario and basins of attraction. The results show the influence of geometry and the nonlinear modal coupling on the nonlinear response of the cylindrical panel.

• Periodical: Applied Mechanics and Materials (Volume 849)
• Pages: 106-118
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.849.106
• Online since: August 2016
• Authors: Frederico Martins Alves da Silva, Henrique Araújo Rodrigues Sattler, Paulo Batista Gonçalves, Zenón José Guzmán Nunñez del Prado
• Keywords: Cylindrical Panels, Modal Coupling, Nonlinear Vibrations

References

[1] A.W. Leissa, A.S. Kadi, Curvature effects on shallow shell vibrations, Journal of Sound and Vibration 16 (1971) 173-187.

DOI: 10.1016/0022-460x(71)90482-2

[2] D. Hui, Influence of geometric imperfections and in-plane constraints on nonlinear vibrations of simply supported cylindrical panels, Journal of Applied Mechanics 51 (1984) 383-390.

DOI: 10.1115/1.3167629

[3] CY. Chia, Nonlinear vibration and postbuckling of unsymmetrically laminated imperfect shallow cylindrical panels with mixed boundary conditions resting on elastic foundation, International Journal of Engineering Science 25 (1987) 427-441.

DOI: 10.1016/0020-7225(87)90069-3

[4] S. Yamada, J.G.A. Croll, Buckling behavior of pressure loaded cylindrical panels, Journal of Engineering Mechanics 115 (1989) 327-344.

DOI: 10.1061/(asce)0733-9399(1989)115:2(327)

[5] A. A. Popov, J.M.T. Thompson, J.G.A. Croll, Bifurcation analyses in the parametrically excited vibrations of cylindrical panels, Nonlinear Dynamics 17 (1998) 205-225.

[6] M. Amabili, Nonlinear vibrations of circular cylindrical panels, Journal of Sound and Vibration 281 (2005) 509-535.

DOI: 10.1016/j.jsv.2004.01.021

[7] F. Alijani, M. Amabili, Nonlinear vibrations of thick laminated circular cylindrical panels, Composite Structures 96 (2013) 643-660.

DOI: 10.1016/j.compstruct.2012.09.016

[8] V.D. Kubenko, P. S. Koval'chuk, Nonlinear problems of the vibration of thin shells (review), International Applied Mechanics 34 (1998) 703-728.

DOI: 10.1007/bf02702126

[9] F. Moussaoui, R. Benamar, Non-linear vibrations of shell-type structures: a review with bibliography, Journal of Sound and Vibration 255 (2002) 161-184.

DOI: 10.1006/jsvi.2001.4146

[10] M. Amabili, M. P. Paidoussis, Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shell and panels, with and without fluid-structure interaction, Applied Mechanics Reviews 56 (2013) 349-381.

DOI: 10.1115/1.1565084

[11] F. Alijani, M. Amabili, Non-linear vibrations of shells: a literature review from 2003 to 2013, International Journal of Non-Linear Mechanics 58 (2014) 233-257.

DOI: 10.1016/j.ijnonlinmec.2013.09.012

[12] H.N. Chu, Influence of large-amplitudes on flexural vibrations of a thin circular cylindrical shell, Journal of Aerospace Science 28 (1961) 602-609.

DOI: 10.2514/8.9113

[13] J. Nowinski, Nonlinear transverse vibrations of orthotropic cylindrical shells, AIAA Journal 1 (1963) 617-620.

DOI: 10.2514/3.1604

[14] D. A Evensen, Some observations on the nonlinear vibration of thin cylindrical shells, AIAA Journal 1 (1963) 2857-2858.

DOI: 10.2514/3.2188

[15] M.D. Olson, Some experimental observations on the nonlinear vibration of cylindrical shells, AIAA Journal 3 (1965) 1775-1777.

DOI: 10.2514/3.55196

[16] E.H. Dowell, C.S. Ventres, Modal equations for the nonlinear flexural vibrations of a cylindrical shell, International Journal of Solids and Structures 4 (1968) 975-991.

DOI: 10.1016/0020-7683(68)90017-6

[17] S. Atluri S, A perturbation analysis of non-linear free flexural vibrations of a circular cylindrical shell, International Journal of Solids and Structures 8 (1972) 549-569.

DOI: 10.1016/0020-7683(72)90022-4

[18] P.B. Gonçalves, R.C. Batista, Nonlinear vibration analysis of fluid-filled cylindrical shells, Journal of Sound and Vibration 127 (1988) 133-143.

DOI: 10.1016/0022-460x(88)90354-9

[19] P.B. Gonçalves, F.M.A. Silva, Z.J.G.N. Prado, Low-dimensional models for the nonlinear vibration analysis of cylindrical shells based on a perturbation procedure and proper orthogonal decomposition, Journal of Sound and Vibration 315 (2008).

DOI: 10.1016/j.jsv.2008.01.063

[20] F.M.A. Silva, P.B. Gonçalves, Z.J.G.N. Prado, An alternative procedure for the non-linear vibration analysis of fluid-filled cylindrical shells, Nonlinear Dynamics 66 (2011) 303-333.

DOI: 10.1007/s11071-011-0037-z

[21] G.W. Hunt, K.A.J. Williams, R.G. Cowell, Hidden symmetry concepts in the elastic buckling of axially loaded cylinders, International Journal of Solid and Structures 22 (1986) 1501-1515.

DOI: 10.1016/0020-7683(86)90058-2

[22] J. Awrejcewicz, A.V. Krys'ko, Analysis of complex parametric vibrations of plates and shells using Bubnov-Galerkin approach, Archive of Applied Mechanics 73 (2003) 495-504.

DOI: 10.1007/s00419-003-0303-8

[23] R. Seydel, From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis, Elsevier Science Publishing, New York, (1988).

[24] M. Amabili, M. Pellegrini, M. Tommesani, Experiments on large-amplitude vibrations of a circular cylindrical panel, Journal of Sound and Vibration 260 (2003) 537-547.

DOI: 10.1016/s0022-460x(02)00959-8

[25] A.H. Nayfeh, B. Balachandran, Applied nonlinear dynamics: analytical, computational and experimental methods, John Wiley & Sons, Inc., (1995).