Nonlinear and chaotic oscillations of pipes conveying fluid under harmonic excitation

The dynamics of a pipe conveying fluid with both ends fixed, excited by the harmonic motion of its supporting base in a direction normal to the pipe span, were investigated theoretically. The nonlinear differential equation of motion of the system was derived by considering the additional axial force due to lateral motion of the pipe. The static equilibria of the pipe deflection were analyzed. Melnikov method was used to predict the initiation of chaotic motions for the case in which three equilibria and a homoclinic orbit exists. The result was compared with that obtained by numerical simulations. It was found that chaotic motions of this system could be born from either intermittent chaos or periodic doubling bifurcations.