Research on vibration control and nonlinear dynamic behavior of railway vehicle systems based on nonlinear energy sinks.

Li, R; Zhao, Y; Liu, Y; Yang, S; Wang, P; Wang, B · 2026 · PubMed Central

DOI: 10.1038/s41598-026-49867-4

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Summary

This study addresses the challenge of suppressing abnormal vibrations in railway vehicle car bodies and bogie frames, which degrade ride comfort and operational safety. While nonlinear energy sinks (NES) have proven effective in other engineering fields, their application in railway vehicles remains limited, particularly regarding coupled vibration reduction across multiple structural components. The authors propose a distributed installation strategy, placing five NES units on both the car body and bogie frames to simultaneously mitigate global vibrations. The researchers established a nine-degree-of-freedom vertical dynamic model of the railway vehicle–NES coupled system based on Newton’s second law. The model accounts for the vertical displacement and pitch angle of the car body, as well as the vertical displacements of the front and rear bogie frames. Five NES units are strategically positioned at the front, middle, and rear of the car body, and on the front and rear bogie frames. The system is subjected to dual harmonic excitations with identical frequencies but different phases, simulating track irregularities. To analyze the system's behavior, the authors derived approximate analytical solutions for amplitude–frequency response curves using the harmonic balance method. These analytical results were verified against numerical simulations performed using the Runge–Kutta method in MATLAB. The study utilized specific structural parameters, including a car body mass of 33,766 kg and NES masses ranging from 228 kg to 1,125 kg, with cubic nonlinear stiffnesses of $5 \times 10^4$ N/m³. The results demonstrate that the distributed installation of NES units effectively suppresses vibrations in both the car body and bogie frames. The analysis of amplitude–frequency response curves, time–history curves, phase trajectories, and Poincaré maps reveals that optimizing NES parameters—specifically mass, damping, and cubic stiffness—further reduces structural vibrations. Crucially, the study identifies that proper parameter tuning helps avoid adverse nonlinear dynamic behaviors, such as bifurcations and chaotic responses, which can occur in NES-coupled systems. The harmonic balance method provided accurate predictions of the system's periodic steady-state responses, confirming the validity of the analytical approach. This research provides fundamental theoretical support for the engineering application of NES in railway vehicles. By demonstrating the efficacy of a distributed multi-NES configuration, the study offers specific guidance for the parameter design of vibration control systems. The findings suggest that this approach can significantly improve the operational stability and ride comfort of high-speed trains by mitigating complex nonlinear dynamic behaviors and ensuring robust vibration suppression across the entire vehicle structure.

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