The Analysis Of Nonlinear Dynamics In The System Of Externally Excited Pipes Conveying Fluid

In this paper, the stability, global bifurcations and chaotic vibrations of a pinned-pinned pipe conveying fluid, excited by the harmonic motions of its supporting base, are investigated theoretically, and the effect of parameters on the nonlinear dynamics of the system is analyzed.The nonlinear equations of motion of the system are derived, and the differential equations are reduced by dimensionless and discretization procedures to obtain the first-order differential equations of the system. The conditions for which the system has zero eigenvalues are discussed, and the relations of the system parameters, such as fluid velocity, mass ratio, external applied tension, for the occurrence of 0:1 internal resonance are obtained. Applying the normal form method of gyroscopic systems, the normal form of equations of motion with 0:1 internal resonance and second mode resonance are obtained. The conditions of existence of Hamiltonian equation are derived for the unperturbed system, and by a series of variable transformations, a near-integrable four-degree-of-freedom Hamiltonian system is obtained.The fixed points and their stabilities of the Hamiltonian system are analyzed. The system parameters for the occurrence of Silnikov homoclinic orbits and heteroclinic orbits are discussed by means of Melnikov method. The phase plane portraits and time history portraits are given at different parameter values of the system to confirm the theoretical result.