Nonlinear vibrations and chaos in floating roofs

Shabani, R ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1115/1.4005437
  3. Publisher: 2012
  4. Abstract:
  5. 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
  6. Keywords:
  7. Sloshing ; Variational principle ; Base excitation ; Bifurcation diagram ; Broadband structures ; Chaotic response ; Cylindrical liquids ; Duffing equations ; Floating roof ; Fractal structures ; Frequency spectra ; Governing equations ; Large deflection ; Lyapunov exponent ; Non-linear model ; Non-linear response ; Non-linear stiffness ; Non-linear vibrations ; Non-Linearity ; Poincare map ; Quantitative criteria ; Resonance harmonics ; Super-harmonic ; Wave elevations ; Control nonlinearities ; Fuel sloshing ; Harmonic analysis ; Lyapunov methods ; Roofs ; Spectroscopy ; Variational techniques ; Nonlinear equations
  8. Source: Journal of Computational and Nonlinear Dynamics ; Volume 7, Issue 2 , January , 2012 ; 15551415 (ISSN)
  9. URL: http://computationalnonlinear.asmedigitalcollection.asme.org/article.aspx?articleid=1397043