Over the last year and a half, the transit draft behavior of the U.S. Navy Mobile Offshore Base (MOB) has been investigated. This has been a multi-faceted effort which has consisted of analytic experimental and numerical approaches. The analytical effort has been completed at the University of New Orleans Marine Dynamics Lab. The model tests have been completed at the U.S Naval Academy's Hydromechanics Lab. The analytical study has also been subdivided into various aspects, which are more completely described in a previous paper (Falzarano, et al., 1999). The focus of this paper is on parametric excitation that results when the top of the lower hull is alternately wetted and dried when a wave passes as the vessel heaves and pitches in head seas. In this work, we investigate the sensitivity of the parametric stability to the representation the radiated wave hydrodynamic force. Specifically, we compare an approximate constant coefficients representation of the radiated wave hydrodynamic force to the more accurate impulse response function representation of the radiated wave hydrodynamic force.
Parametric or internal excitation results when one of the motion variables in the differential equation varies with time. This differs from external or direct excitation where the excitation is purely timevarying and does not involve the motion variables or coefficients (Francescntto, 2000). Direct or external excitation is the more familiar type of excitation and results in the dynamic magnification curve from elementary vibration theory. The direct excitation magnification curve is exemplified by the peak at resonance. Depending upon the relative amount of damping, the peak is large or insignificant but always occurs when the forcing frequency is equal to the natural frequency. Alternatively, the parametric resonance occurs at various fractions and multiples of the natural frequency most notably at the dominant subharmonic resonance.
