APPLICATION OF MELNIKOV METHOD IN THE STUDY OF CHAOTIC MOTIONS OF PIPE CONVEYING FLUID

The chaotic vibrations of a clamped-clamped pipe conveyingfluid, excited by the harmonic motions of its supporting base, wereinvestigated theoretically. The nonlinear equations of motion were derived,and the equilibrium and stabilities of the system were analyzed. Theexpressions of homoclinic orbits of the unperturbed system were calculated.The system parameters for the occurrence of chaotic motionswere obtained by means of Melnikov method. Phase portrait and Poinc\'aremap were used to simulate the chaotic motions of the original system.Comparison between the results from theoretical analyses and numericalsimulations reveals that the critical value of the parameter determined byMelnikov method is slightly lower than that corresponding to the chaoticmotion observed first in numerical simulations.