Prediction of frequency response of sub-frame bushing and study of high-order fractional derivative viscoelastic model

Abstract

This paper presents experimental and dynamic modeling research on the rubber bushings of the rear sub-frame. The Particle Swarm Optimization algorithm was utilized to optimize a Backpropagation (BP) neural network, which was separately trained and tested across two frequency ranges: 1–40 Hz and 41–50 Hz, using wideband frequency sweep dynamic stiffness test data. The testing errors at amplitudes of 0.2 mm, 0.3 mm, and 0.5 mm were found to be 1.03%, 3.05%, and 1.96%, respectively. Subsequently, the trained neural network was employed to predict data within the frequency range of 51–70 Hz. To incorporate the predicted data into simulation software, a dynamic model of the rubber bushing was established, encompassing elastic, friction, and viscoelastic elements. Additionally, a novel model, integrating high-order fractional derivatives, was proposed based on the frequency-dependent model for the viscoelastic element. An enhanced Particle Swarm Optimization algorithm was introduced to identify the model's parameters using the predicted data. In comparison to the frequency-dependent model, the new model exhibited lower fitting errors at various amplitudes, with reductions of 3.84%, 3.61%, and 5.49%, respectively. This research establishes a solid foundation for subsequent vehicle dynamic modeling and simulation.