Bifurcation Analysis of Nonlinear Vehicle System under Road Excitation

路面激勵下非線性汽車模型之分岔分析

童林軍(Lin-Jun Tong) ； 楊岳(Yue Yang) ； 黃惠媛(Hui-Yuan Huang) ； 李秋娥(Qiu-E Li) ； 陳峰(Feng Chen) ； 李雄兵(Xiong-Bing Li)

《中國機械工程學刊》 34卷4期 (2013/08) Pp. 313-320

摘要

本文提出了一種新的遲滯接觸力模型來模擬汽車在受路面激勵時的振動特性。通過計算分岔圖、相圖和吸引子研究了該系統的倍周期分岔、硬彈簧特性及多解共存問題。利用胞映射方法研究了該系統的全局動力學特性。雖然與真實地試驗汽車振動相比，模型比較簡化。但是該模型在模擬輪胎脫離裏面時的接觸力模型更加精確。研究結果表明路面激勵對汽車振動響應有非常大的影響。當汽車行駛在低等級路面時，系統振動存現非線性特征。當汽車行駛在高等級公路時，系統振動表現為線性特征。研究證實在該類系統中存現出倍周期分岔過程、硬彈簧特性及多解共存的特征。

並列摘要

A new hysteresis contact force model is proposed to simulate the vibration characteristics with road profile excitation. The dynamic characteristics, period doubling bifurcation, hardening type nonlinearity and the coexisting of periodic solutions are studied numerically with bifurcation map, phase portraits and basin of attractor. The cell mapping method is introduced to study the global characteristics of the quarter car vibrations. The quarter car model used in this paper is very simple and would not be sufficient to simulate the detailed response of a vehicle especially directly comparing to the experimental results. However the proposed model is more realistic especially when the road profile excitation is large and the tire loss contact with road surface. The numerical results show that the vibration characteristics of the car vibration system are mainly determined by the road profile excitation parameters. When the car moves on a minor road, it presents nonlinear characteristics. But as for the motorway, the road profile excitation amplitude is low, and the car vibration system is more likely to exhibit linearly characteristics. The period doubling bifurcation, well-know hardening type nonlinearity and the co-existing of stable periodic solutions are detected in the presented model.

並列關鍵字

bifurcation ； vehicle system ； cell mapping