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Dynamics of neutrally buoyant inflatable structures used in submarine detection Misra, Arun Kanti

Abstract

The dynamics of a submarine detection system using neutrally buoyant inflated structural members is investigated with mathematical models representing increasing order of complexity. An appreciation of the flexural deflections of a single inflated viscoelastic cylindrical cantilever is first gained using the three parameter solid model. This is followed by its free vibration analysis in the presence of hydrodynamic forces and axial tension arising due to the internal pressure. The approximate solutions of the governing nonlinear, partial differential equation are substantiated through numerical and experimental data. An analysis of dynamical response to the surface wave excitations provides useful design information. Next, the coupled motion of an array consisting of three legs and a central head is studied. The inplane and out of plane motions, which essentially decouple for small oscillations, are considered separately. Effects of the inflation pressure and inertia parameters on the natural frequencies of the system are examined and the possibility of dynamic instability for certain parametric values established. The vertical motion of a buoy-cable-array assembly is considered subsequently. The cable is replaced by a spring of equivalent stiffness and the flexural displacements of the legs are superposed on the motion of the central head. The free vibration of the system is studied first and the influence of the important system parameters on the natural frequencies evaluated. The motion excited by a sinusoidal surface wave is also studied to explore the possibility of reducing the tip displacements. The dynamics of a buoy-cable-array assembly drifting with a uniform velocity is then investigated. As the motion is rather complex because of the large number of degrees of freedom involved, a relatively simple model is considered to obtain some appreciation of the problem. The oscillations of the buoy and flexibility of the legs are ignored and the cable is represented by two straight lines. The steady state configurations of this system and their dependence on various parameters are examined. The double pendulum type motion of the cable along with the rotational oscillations of the array around the equilibrium positions are studied to obtain preliminary information regarding the stability of the motion. Reduction in the length or diameter of the arms appears to improve the damping rates of the system. Finally, some of the restrictions inherent in the simplified model are removed. The flexibility of the legs and the tangential drag which were neglected earlier, are taken into account. A more accurate cable configuration is considered to make the model closer to the reality. However, the oscillations of the buoy are again ignored. With this, the steady state configurations of the system are determined around which a linearized perturbation analysis is carried out. Longitudinal and lateral motions essentially decouple for small amplitude motions. Natural frequencies of the system are found by analyzing the resulting eigenvalue problem and the influence of various parameters on the damping of the disturbances examined. As noticed in the rigid array analysis, shorter arm lengths improve the decaying characteristics of the system. But the minimum acceptable length being governed by the signal processing considerations, a compromise is indicated in the design. For given cable and arm lengths, there appears to be an optimum diameter from the stability considerations.

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