Nonlinear dynamics of low order models of offshore structures
Abstract
The dynamic response of a structure with nonlinear stiffness characteristics and excited by a non-zero mean oscillatory fluid flow is investigated. Three different models of the offshore structures, with one and two degrees of freedom, are studied in this research. Various steady-state responses of the system are obtained by four different solution techniques. Floquet theory as well as direct numerical integration are utilized to examine the stability of these solutions. For the one-dimensional model with linear and cubic stiffness, the results clearly show that near secondary resonances, the response to a single frequency input contains many harmonics, and therefore the standard method of averaging and the equivalent linearization technique are not adequate for an accurate representation of these solutions. Large primary and superharmonic resonances are found to exist. The one-dimensional model with bilinear stiffness exhibits several subharmonic resonances. In addition, period-doubling bifurcations and co-existent stable steady-state solutions are observed. Boundary crisis seems to eliminate the period-doubled solutions over some frequency intervals. Finally, the solutions of a two-degree-of-freedom model with linear and cubic stiffness are studied. The effect of varying the incidence direction of the regular wave as well as the coupling between steady current and regular wave are presented. When the current and the wave are incident from a single direction and the damping is sufficiently small, the planar motion is unstable near primary resonance and biplanar motion arises. This biplanar motion can be harmonic, periodic amplitude-modulated or chaotic amplitude-modulated response. The nonperiodic solutions may disappear due to the presence of crisis phenomenon. In general, the presence of steady current results in hysteresis and asymmetry in the resonances and a large drag force tends to suppress the various resonances.
Degree
Ph.D.
Advisors
Bajaj, Purdue University.
Subject Area
Mechanical engineering
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