Impact vibration response of simply supported fluid-conveying pipes with a rigid constraint under multi-source excitation

The dynamic behavior of fluid-conveying pipes can lead to significant safety hazards when subjected to impact vibrations, influenced by complex operational environments such as base excitations, distributed follower forces, and support looseness. A model for the impact vibration of a simply supported, rigidly constrained fluid-conveying pipe is established based on Hamilton’s principle under the combined effects of base excitations and distributed follower forces. The Galerkin method and the NDFs (variable-order numerical differentiation formulas) algorithm are employed for discretizing and solving the equation, respectively. The influences of parameters on the model are discussed under the actions of the base excitation frequency, magnitude of distributed follower forces, and fluid velocity. The evolutionary pathways within the model the periodic motions, quasi-periodic motions, chaos are captured by the analysis of bifurcation diagrams, phase diagrams, Poincaré maps, and time-history curves. So are unique behaviors to rigid impacts such as chatter vibrations and wiping contacts, and the stable focus on the Poincaré map mutates into an attractor with a shape resembling a plum blossom under multi-source excitation. The research reveals that Plum blossom attractors provide critical transition markers for analyzing vibration evolution from stable focus to attracting circles. Low base excitation frequencies trigger chatter-impact vibrations. The findings of this study provide a theoretical basis for the engineering parameter settings or safe operation of fluid-conveying pipes under multi-source excitation.