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Dynamics of neutrally buoyant inflatable viscoelastic cantilevers in the ocean environment Poon, David Tat-Sang

Abstract

Statics and dynamics of the neutrally buoyant inflated viscoelastic cantilevers constituting a submarine detection system is investigated. Two geometries of the thin-walled beams are considered: uniform circular cylindrical and circular tapered. The static flexural behaviour of the beam is studied using the three parameter viscoelastic solid model which yields material properties for the mylar-polyethylene-mylar plastic film used. Results of a detailed experimental program are also presented to substantiate validity of the analytical model. This is followed by free vibration analyses of the inflated cantilevers in the ocean environment accounting for the added inertia and nonlinear hydrodynamic drag. For the uniform cylindrical beam, thin-shell theories are employed to account for the inflation effects on the free vibration characteristics. A significant feature of the analysis is the reduction of the shell equations (the membrane, Fliigge's, and Herrmann-Armenakas') into a single equation which is similar in form to that for a vibrating beam with rotary inertia effects. The natural frequencies obtained are compared with the experimental results and those predicted by the Rayleigh-Ritz method in conjunction with the Washizu and membrane shell theories. The analyses show, and experimental program confirms, that Fliigge's shell equation in the reduced form is capable of predicting free vibration behaviour quite accurately. However, the reduction technique should be applied with care, since in several cases it leads to misleading results (e.g. in the case of Herrmann-Armenakas theory). For the tapered case the elementary beam theory is used to predict their natural frequencies. Next, the dynamical response of the uniform and tapered cantilevers to root excitation, at the fundamental wave frequency and its second harmonic, is studied. The governing nonlinear equations are analyzed by taking two terms of the assumed Fourier series solution. Results suggest that for the case of the simple harmonic excitation, the nonlinear hydrodynamic drag introduces no superharmonic components into the response. For low forcing frequencies typical of the ocean environment, an increase in taper ratio tends to reduce the tip amplitudes. However, for frequencies above the fundamental, the response characteristics are completely reversed. The analysis provides valuable information concerning the system parameters leading to critical response and hence should prove useful in the design of inflatable members employed in the submarine detection system.

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