Non-stability of a bogie moving along a specific infinite complex flexibly beam-layer structure

Abstract

A comprehensive investigation was conducted to analyze the vibration stability of a bogie that moves uniformly along a complexly modeled flexibly supported infinite Reddy-Bickford coupled beam system situated on a viscoelastic base. The bogie was simulated as a non-deformable body of finite length, connected through a specific system of two springs and two dampers with identical stiffness and damping, interacting with masses within a complex beam-layer system commonly encountered in technical practice. These masses, through which the bogie interacts with the high-order shear deformable beam-layer system, form part of a mechanical system consisting of a double oscillator in constant contact with the infinitely long flexible structure. As it is well-known that when the velocity of masses, such as the bogie or any other complex oscillator, exceeds the minimum velocity at which waves propagate in the beam, the system's oscillation may become unstable, it is crucial to determine the conditions and stable regions of motion that involve specific combinations of system parameters. The region of instability is identified within the parameter space of the system using the D-decomposition technique and the argument principle. A comprehensive analysis was conducted to investigate the impacts of the viscous damping in the supports of the bogie, the mass of the bogie bar, and the wheelbase on the stability of the model. The derived conclusions, focused on determining the stable regions of motion based on the considered parameters, represent a significant novelty and contribution to the research previously unknown for the motion system of a bogie along a complexly modeled flexibly supported infinite high-order shear deformable coupled beam-layer system on a viscoelastic base.