LARGE AMPLITUDE VIBRATIONS OF CIRCULAR CYLINDRICAL SHELLS

1996 ◽  
Vol 192 (1) ◽  
pp. 1-14 ◽  
Author(s):  
M. Ganapathi ◽  
T.K. Varadan
Keyword(s):  
Large Amplitude ◽  
Cylindrical Shells ◽  
Circular Cylindrical Shells ◽  
Large Amplitude Vibrations

Comparison of Different Shell Theories for Large-Amplitude Vibrations of Circular Cylindrical Shells

2002 ◽  
Author(s):  
M. Amabili
Keyword(s):  
Large Amplitude ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Continuation Method ◽  
Elastic Strain Energy ◽  
Harmonic Excitation ◽  
Lagrange Equations ◽  
Simply Supported ◽  
Nonlinear Shell ◽  
Circular Cylindrical Shells

Large-amplitude (geometrically nonlinear) vibrations of circular cylindrical shells subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated. The Lagrange equations of motion are obtained by an energy approach, retaining damping through Rayleigh’s dissipation function. Four different nonlinear shell theories, namely Donnell’s, Sanders-Koiter, Flu¨gge-Lur’e-Byrne and Novozhilov’s theories, are used to calculate the elastic strain energy. The formulation is also valid for orthotropic and symmetric cross-ply laminated composite shells. The large-amplitude response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of the lowest natural frequency is computed for all these shell theories. Numerical responses obtained by using these four nonlinear shell theories are also compared to results obtained by Galerkin approach, used to discretise Donnell’s nonlinear shallow-shell equation of motion. A validation of calculations by comparison to experimental results is also performed. Boundary conditions for simply supported shells are exactly satisfied. Different expansions involving from 14 to 48 generalized coordinates, associated to natural modes of simply supported shells, are used. The nonlinear equations of motion are studied by using a code based on arclength continuation method that allows bifurcation analysis.

Large amplitude vibrations of anisotropic cylindrical shells

2004 ◽  
Vol 82 (23-26) ◽  
pp. 2015-2025 ◽  
Author(s):  
M.H. Toorani ◽  
A.A. Lakis
Keyword(s):  
Large Amplitude ◽  
Cylindrical Shells ◽  
Large Amplitude Vibrations
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