The nonlinear dynamics of towed array lifting devices

The use of passive towed sonar arrays in submarines results in improved detection capabilities. The need to understand the dynamics of such a towed array is the motivation for this work. The simple case of a plate towed in water is examined in this thesis. The plate is assumed to move only in the horizontal direction perpendicular to the tow direction. The tension in the tow cable is expected to vary with time as a result of turbulent forces produced in the boundary layer along the towline. These forces are modeled as a sinusoid, resulting in the governing differential equation x&d3;+d +ecostx +x&d2; x&d2; =0, 1 where x is the direction perpendicular to the tow direction.; The differential equation, a nonlinear Mathieu equation, is analyzed with linear stability analysis to find the stability of the origin. A nonlinear analysis is performed for small values of ε by the method of averaging. Periodic solutions are identified and their stability determined. Numerical analysis of the differential equation is used to identify a secondary bifurcation at values of ε near unity and chaos in the system near ε = 3.; A perturbation method is developed to characterize the secondary bifurcation. The method involves perturbing off of the linear Mathieu equation itself. The method yields approximations to the bifurcation curve, the solution to the differential equation, and the amplitude of the periodic motion.; The bifurcations, periodic motions, and other dynamical features are related to the physical problem of the towed sonar array. A control strategy which takes advantage of the secondary bifurcation to remove unwanted oscillations is presented. This strategy involves retracting and then deploying the cable.