Parametric excitation of the DWSC (Deep Water Stable Craneship) is studied in this thesis. It occurs for a system without any external forcing, when one of the coefficients in the equation of motion (EOM) modeling the system varies with time. Parametric instability might be triggered for certain values of the parameters describing the time-varying coefficient. The DWSC, basically a stepped classic spar with a catamaran as its deck, because of certain unique features, may be susceptible to parametric excitation. This thesis examines the phenomenon of parametric excitation with respect to roll motion in head seas, using time-domain simulation and stability analysis. It examines the DWSC's susceptibility to parametric instability using the same methods of analysis and the effect of damping (especially viscous drag) on parametric excitation and instability. The thesis uses Mathieu's equation as the basis for stability analysis and time-simulates the coupled heave-sway-roll EOM. Time-domain simulation is done for two reasons: firstly for determining the variation in roll stiffness because of a regular wave (the variation in roll stiffness is an input to the stability analysis) and secondly for simulating the coupled heave-sway-roll EOM. Both time-domain analysis and stability analysis are done for sea states of interest and for examining interesting phenomena like roll resonance (due to body-wave interaction) and parametric instability. Results highlight: 1) a "cancellation frequency" in the heave wave exciting force; 2) the effect of viscous drag on coupled heave-sway-roll motions; 3) time-simulations validating the stability analysis; 4) the trend of stability with increasing sea states, wave periods and amplitudes; 5) characteristics of parametric instability; 6) the methodology used to predict or detect parametric instability and 7) the effect of viscous drag on parametric instability.
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