Nonlinear Dynamics of Two-Degrees-of-Freedom Fluid Conveying Elasto-Visco-Plastic Model System

Abstract

The local and global nonlinear dynamics of a two-degrees-of-freedom model system conveying fluid is studied. The undeflected model consistsof an inverted T formed by three rigid rods, with the tips of the twohorizontal rods resting on the viscous foundation. The foundationexhibits a visco-elasto-plastic response, including the Bauschingereffect. The vertical rigid rod of an annular cross-section is subjectedto a conservative (dead) force. Also, it conveys fluid having bothstatic and pulsation components. First, the method of multiple scales isused for the analysis of the local dynamics of the system withvisco-elastic response. Attention is focused on modal interactionphenomena in weak excitation at primary resonance and on hardsub-harmonic excitation. Two different asymptotic expansions areutilised to get a structural response for typical ranges of excitationparameters. Numerical integration of the governing equations is thenperformed to validate the results of asymptotic analysis in each case. Afull global nonlinear dynamics analysis of the visco-elasto-plasticsystem is performed. The role of plastic deformations in thedestabilisation of the system is discussed. Large-amplitude nonlinearoscillations of the visco-elasto-plastic system are studied, includingthe influence of material hardening and of static and periodiccomponents of pulsating fluid. Chaotic regimes of motion with andwithout plastic effects are considered. The results of the analysis maybe used in devices composed of a rather short tube connected to a notcompletely fixed foundation resting on the soil exhibitingelasto-plastic behaviour.