Variational principle is used to derive the nonlinear response of the floating roof of cylindrical liquid storage tanks due to harmonic base excitations. The formulation accounts for nonlinearity due to large deflections of the floating roof. The derived nonlinear governing equation for the sloshing response of the floating roof has a cubic nonlinear stiffness term similar to the well known Duffing equation. It is shown that accounting for large deflections could substantially reduce the wave elevation for near resonance harmonic excitations. Evaluating the response of the nonlinear model for increasing amplitudes of near resonance harmonic excitations gives rise to the appearance of sub and super harmonics in the response. The broadband structure of the frequency spectrum, the fractal structure of the Poincare maps, and the bifurcation diagram as qualitative criteria and Lyapunov exponent evolution as quantitative criterion are used to investigate the emergence of chaotic response.
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e-mail: r.shabani@urmia.ac.ir
e-mail: s.tariverdilo@urmia.ac.ir
e-mail: salarieh@sharif.edu
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April 2012
Research Papers
Nonlinear Vibrations and Chaos in Floating Roofs
R. Shabani,
R. Shabani
Mechanical Engineering Department,
e-mail: r.shabani@urmia.ac.ir
Urmia University
, Urmia 15311-57561, Iran
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S. Tariverdilo,
S. Tariverdilo
Civil Engineering Department,
e-mail: s.tariverdilo@urmia.ac.ir
Urmia University
, Urmia 15311-57561, Iran
Search for other works by this author on:
H. Salarieh
H. Salarieh
Mechanical Engineering Department,
e-mail: salarieh@sharif.edu
Sharif University of Technology
, Tehran 11155-9567, Iran
Search for other works by this author on:
R. Shabani
Mechanical Engineering Department,
Urmia University
, Urmia 15311-57561, Iran
e-mail: r.shabani@urmia.ac.ir
S. Tariverdilo
Civil Engineering Department,
Urmia University
, Urmia 15311-57561, Iran
e-mail: s.tariverdilo@urmia.ac.ir
H. Salarieh
Mechanical Engineering Department,
Sharif University of Technology
, Tehran 11155-9567, Iran
e-mail: salarieh@sharif.edu
J. Comput. Nonlinear Dynam. Apr 2012, 7(2): 021012 (13 pages)
Published Online: January 10, 2012
Article history
Received:
May 16, 2011
Revised:
October 24, 2011
Accepted:
October 25, 2011
Online:
January 10, 2012
Published:
January 10, 2012
Citation
Shabani, R., Tariverdilo, S., and Salarieh, H. (January 10, 2012). "Nonlinear Vibrations and Chaos in Floating Roofs." ASME. J. Comput. Nonlinear Dynam. April 2012; 7(2): 021012. https://doi.org/10.1115/1.4005437
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