Nonlinear Ship Dynamics
Final rept. 1 Mar 1983-30 Nov 1990
VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF ENGINEERING SCIENCE AND MECHANICS
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The contract effort is theoretical and experimental investigation of a the nonlinear response of ships in regular and irregular waves and b means of controlling complicated and large-amplitude oscillations. Some of the new analytical techniques developed in applied mathematics and nonlinear dynamics have been adapted for ships motions. These techniques include perturbation techniques, bifurcation theory, renormalization techniques, Poincare maps, fractal concepts, knot theory, nonlinear form theory, cell-to-cell mapping, symbolic manipulators, invariant measures, and Melnikov theory. Moreover, a number of recent discoveries in nonlinear dynamics have been carried over into ship motions. For example, we have shown that the nonlinearity brings a whole range of phenomena in the rolling motion of biased and unbiased ships in regular seas. These phenomena include coexistence of attractors long-time responses, jumps between coexisting attractors, period-multiplying bifurcations, sensitivity of response to initial conditions, chaotic motions, and capsizing. When the pitch frequency is approximately twice the roll frequency, we have shown theoretically that the ship has undesirable seakeeping characteristics, as noted by Froude in 1963. We have also shown that the ship motion can be very complicated even if the waveslopes are extremely small. The complicated motions include saturation, amplitude- and phase-modulated motions, and chaotic motions.
- Marine Engineering
- Fluid Mechanics