Nonlinear dynamics of an underwater slender beam with two axially moving supports

This paper investigates the nonlinear dynamic behavior of a towed underwater beam with two supported ends. The equation of motion is derived by the Newtonian approach. An “axial added mass coefficient” is taken into account to get a better approximation for the mass of fluid attached to beams. Nonlinear deflection-dependent axial forces are also considered. The dynamics of the system is studied via Galerkin approach and Runge-Kutta technique. The linear dynamic analysis is conducted firstly. The solution for natural frequency is obtained and the result shows that the beam will subject to buckling-type instability if the moving speed exceeds a certain value. Then, the buckled configuration is obtained and its stability is discussed in the nonlinear dynamic analysis. It is found that the subcritical Hopf bifurcation of the first buckled mode may occur when the towing speed reaches to a critical value. In addition, the nonlinear dynamic responses are calculated and the periodic-1, period-3, period-5, quasi-periodic and chaotic motions are detected. Meanwhile, the result shows the route to chaos for the beam is via period-3 motions or quasi-periodic motions. The effects of several system parameters on the chaotic motion are also studied.