Nonlinear dynamics of two-degrees-of-freedom fluid conveying elasto-visco-plastic model system

摘要

The local and global nonlinear dynamics of a two-degrees-of-freedom model system conveying fluid is studied. The undeflected model consists of an inverted T formed by three rigid rods, with the tips of the two horizontal rods resting on the viscous foundation. The foundation exhibits a visco-elasto-plastic response, including the Bauschinger effect. The vertical rigid rod of an annular cross-section is subjected to a conservative (dead) force. Also, it conveys fluid having both static and pulsation components. First, the method of multiple scales is used for the analysis of the local dynamics of the system with visco-elastic response. Attention is focused on modal interaction phenomena in weak excitation at primary resonance and on hard sub-harmonic excitation. Two different asymptotic expansions are utilised to get a structural response for typical ranges of excitation parameters. Numerical integration of the governing equations is then performed to validate the results of asymptotic analysis in each case. A full global nonlinear dynamics analysis of the visco-elasto-plastic system is performed. The role of plastic deformations in the destabilisation of the system is discussed. Large-amplitude nonlinear oscillations of the visco-elasto-plastic system are studied, including the influence of material hardening and of static and periodic components of pulsating fluid. Chaotic regimes of motion with and without plastic effects are considered. The results of the analysis may be used in devices composed of a rather short tube connected to a not completely fixed foundation resting on the soil exhibiting elasto-plastic behaviour. [References: 21]