A nonlinear rubber spring model containing fractional derivatives for use in railroad vehicle dynamic analysis

Abstract

A nonlinear dynamic model for a rubber spring is created and subsequently used to describe the mechanical behavior of rubber mounts in the suspension system of a railroad vehicle. The characteristics of dynamic stiffness and damping relative to the applied displacement amplitude and frequency are investigated both through simulations and measurements. The model is one dimensional and is based on a superposition of elastic force, frictional force and fractional derivative viscous force. The amplitude dependence is represented by a nonlinear frictional component and a fractional derivative calculus approach is used to account for its frequency dependence. The fractional calculus approach considers previous responses in the current calculation, which results in the memory characteristics of rubber being considered. A linear elastic spring component is still needed to describe its static behavior. The least-squares technique is used to obtain model parameters from measurements, and an overall good agreement between the simulations and measurements is obtained. The model only has five parameters and represents a reasonable compromise between accuracy and computational effort, and thus, it is a suitable tool for railroad vehicle dynamics analysis and simulation.