Nonlinear dynamics of an inclined FG pipe conveying pulsatile hot fluid

In this theoretical work, the nonlinear dynamics of a pinned-pinned inclined functionally graded (FG) pipe conveying pulsatile hot fluid is investigated. The equation of motion of the FG pipe is derived based on the Euler-Bernoulli beam theory and plug-flow model, and that is subsequently solved using Galerkin discretization in conjunction with the incremental harmonic balance/Runge-Kutta method. First, the divergence of the FG pipe is investigated where it is mainly revealed that the inclination of the pipe with the vertical axis yields buckling at a higher temperature while the type of the associated bifurcation changes from pitchfork to saddle-node bifurcation. On the basis of this static instability, the pre- and post-buckled equilibriums of the inclined FG pipe are identified, and its nonlinear dynamics associated with each of these equilibrium states is subsequently studied based on the variations of some system parameters namely inclination angle, temperature, graded exponent of FG material, mean flow velocity, amplitude of pulsatile flow velocity and material damping. The corresponding results reveal some notable nonlinear dynamic characteristics of the inclined FG pipe like the appearance of both the principal primary and secondary parametric resonances in the pre-buckled state, exchange between softening and hardening structural behavior through period doubling/period demultiplying/fold bifurcation, movement of saddle periodic orbit with temperature leading to the unequal domains of attraction over the post-buckled equilibriums and the appearance higher order parametric resonances at low material damping.