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Mechanics in Engineering ›› 2004, Vol. 26 ›› Issue (2): 0-0.doi: 10.6052/1000-0992-2003-040

• Education Study •    

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

  

  • Received:2003-02-05 Revised:2003-05-22 Online:2004-04-10 Published:2004-04-10

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

Key words: Melnikov method, pipe conveying fluid, chaotic motion,