Nonlinear nonplanar dynamics of porous functionally graded pipes conveying fluid

Abstract

This paper aims to investigate the three-dimensional (3-D) nonlinear dynamics of a porous functionally graded (FG) pipe subjected to lateral harmonic excitation. Material properties of the porous pipe are graded across the radius in a power-law distribution form. Based on the Euler–Bernoulli beam theory, the nonlinear equations of motion are derived employing the Hamilton’s principal to achieve third-order accuracy with the fluid-related loads associated with the bending–torsional vibration. The new nonlinear model, consisting of three strongly coupled nonlinear partial differential equations, is discretized into second-order ordinary differential equations via Galerkin method. Subsequently, the pseudo-arclength continuation technique together with a direct time-integration method are employed to perform nonlinear static and dynamic responses of this gyroscopic system. Numerical parametric investigations are conducted to assess the significant effects of different parameters on the resonant dynamic behavior of system, with special focus on the modal interaction that could lead to multiple coexisting solutions including planar and nonplanar motions. Moreover, the nonplanar resonance behavior is revealed that the influences of structural symmetries and symmetry-breaking effects on bifurcations and instabilities in comparison to the previously classical planar resonance behavior.