Nonlinear responses of a fluid-conveying pipe embedded in nonlinear elastic foundations

ABSTRACT nlinear responses of planar motions of a uid-conveying pipe embedded in nonlinear elastic foundations are investigated via the differential quadrature method discretization (DQMD) of the governing partial differential equation. For the analytical model, the effect of the nonlinear elastic foundation is modeled by a nonlinear restraining force. By using an iterative algorithm, a set of ordinary differential dynamical equations derived from the equation of motion of the system are solved numerically and then the bifurcations are analyzed. The numerical results, in which the existence of chaos is demonstrated, are presented in the form of phase portraits of the oscillations. The intermittency transition to chaos has been found to arise.