The fractional differential equations of the single-degree-of-freedom (DOF) quarter vehicle with a magnetorheological (MR) suspension system under the excitation of sine are established, and the numerical solution is acquired based on the predictor–corrector method. The analysis of phase trajectory, time domain response, and Poincaré section shows that the nonlinear dynamic characteristics between fractional and integer-order suspension systems are quite different, which proves the superiority of using fractional order to describe the physical properties. By discussing the influence of each parameter on the vibration, the range of parameters to avoid the chaotic vibration is obtained. The variable feedback control is used to control the chaotic vibration effectively.
Issue Section:
Research Papers
References
References
1.
Sreekar Reddy
, M. B. S.
Vigneshwar
, P.
Sita Ram
, M.
Raja Sekhar
, D.
Sai Harish
, Y.
2017
, “Comparative Optimization Study on Vehicle Suspension Parameters for Rider Comfort Based on RSM and GA
,” Mater. Today
, 4
(2 Part A
), pp. 1794
–1803
.2.
Bouazara
, M.
Richard
, M. J.
Rakheja
, S.
2006
, “Safety and Comfort Analysis of a 3-D Vehicle Model With Optimal Non-Linear Active Seat Suspension
,” J. Terramech.
, 43
(2
), pp. 97
–118
.3.
Naik
, R. D.
Singru
, P. M.
2011
, “Resonance, Stability and Chaotic Vibration of a Quarter-Car Vehicle Model With Time-Delay Feedback
,” Commun. Nonlinear Sci. Numer. Simul.
, 16
(8
), pp. 3397
–3410
.4.
Fakhraei
, J.
Khanlo
, H.
Dehghani
, R.
2017
, “Nonlinear Dynamic Behavior of a Heavy Articulated Vehicle With Magnetorheological Dampers
,” ASME. J. Comput. Nonlinear Dynam
, 12
(4
), p. 041017
.5.
Abtahi
, S. M.
2016
, “Chaotic Study and Chaos Control in a Half-Vehicle Model With Semi-Active Suspension Using Discrete Optimal Ott-Grebogi-Yorke Method
,” Proc. Inst. Mech. Eng. Part K
, 231
(1
), pp. 148–155.6.
Zhang
, W.
Li
, J.
Zhang
, K.
Cui
, P.
2013
, “Design of Magnetic Flux Feedback Controller in Hybrid Suspension System
,” Math. Prob. Eng.
, 2013
, p. 712764.7.
Chen
, Q. T.
Huang
, Y. J.
Song
, Y. R.
2014
, “Modeling and Analysis of High-Order MR Vibration System Based on Fractional Order
,” Chin. J. Sci. Instrum.
, 35
(12
), pp. 2761
–2771
.8.
Turnip
, A.
Park
, S.
Hong
, K. S.
2010
, “Sensitivity Control of a MR-Damper Semi-Active Suspension
,” Int. J. Precis. Eng. Manuf.
, 11
(2
), pp. 209
–218
.9.
Liem
, D. T.
Truong
, D. Q.
Ahn
, K. K.
2015
, “Hysteresis Modeling of Magneto-Rheological Damper Using Self-Tuning Lyapunov-Based Fuzzy Approach
,” Int. J. Precis. Eng. Manuf.
, 16
(1
), pp. 31
–41
.10.
Mainardi
, F.
2010
, “Fractional Calculus and Waves in Linear Viscoelasticity
,” Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models
, Imperial College Press
, London.11.
Wang
, Z. H.
2011
, “Fractional Calculus: A Mathematical Tool Describing the Memory Characteristics and Intermediate Processes
,” Scientific Chinese
, 3
, pp. 76–78.12.
Sun
, H. L.
Jin
, C.
Zhang
, W. M.
Li
, H.
Tian
, H. Y.
2014
, “Modeling and Tests for a Hydro-Pneumatic Suspension Based on Fractional Calculus
,” J. Vib. Shock
, 33
(17
), pp. 167
–172
; 190.13.
Spanos
, P. D.
Evangelatos
, G. I.
2010
, “Response of a Nonlinear System With Restoring Forces Governed by Fractional Derivatives: Time Domain Simulation and Statistical Linearization Solution
,” Soil Dyn. Earthquake Eng.
, 30
(9
), pp. 811
–821
.14.
Machado
, J. A. T.
Silva
, M. F.
Barbosa
, R. S.
Jesus
, I. S.
Reis
, C. M.
Marcos
, M. G.
Galhano
, A. F.
2010
, “Some Applications of Fractional Calculus in Engineering
,” Math. Prob. Eng.
, 2010
, p. 639801
.15.
Scherer
, R.
Kalla
, S. L.
Tang
, Y.
Huang
, J.
2011
, “The Grünwald–Letnikov Method for Fractional Differential Equations
,” Comput. Math. Appl.
, 62
(3
), pp. 902
–917
.16.
Chen
, B. S.
Huang
, Y. J.
2009
, “Application of Fractional Calculus on the Study of Magnetorheological Fluids' Characterization
,” J. Huaqiao Univ.
, 5
, p. 003.17.
Atan
, O.
Chen
, D.
Türk
, M.
2016
, “Fractional Order PID and Application of Its Circuit Model
,” J. Chin. Inst. Eng.
, 39
(6
), pp. 695
–703
.18.
Dimeas
, I.
Tsirimokou
, G.
Psychalinos
, C.
Elwakil
, A. S.
2017
, “Experimental Verification of Fractional-Order Filters Using a Reconfigurable Fractional-Order Impedance Emulator
,” J. Circuits Syst. Comput.
, 26
(09
), p. 1750142
.19.
Kai
, D.
Ford
, N. J.
Freed
, A. D.
2002
, “A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations
,” Nonlinear Dyn.
, 29
(1–4
), pp. 3
–22
.20.
Feng
, Y. L.
Wang
, J. H.
Rai
, Z. P.
Zhou
, Z.
2014
, “Estimation and Correction of Fractional Calculus and Its Application
,” J. Nantong Univ. (Nat. Sci. Ed.)
, 13
(1
), pp. 76
–80
.21.
Zhang
, Q.
Wang
, B. H.
2002
, “Chaos Control With Variable Feedback in Power System
,” Electr. Power Autom, Equip.
, 23
(11
), pp. 9
–12
.22.
Petráš
, I.
2009
, “Chaos in the Fractional-Order Volta's System: Modeling and Simulation
,” Nonlinear Dyn.
, 57
(1
), pp. 157
–170
.23.
Shojaeefard
, M. H.
Khalkhali
, A.
Safarpour Erfani
, P.
2014
, “Multi-Objective Suspension Optimization of a 5-DOF Vehicle Vibration Model Excited by Random Road Profile
,” Int. J. Adv. Des. Manuf. Technol.
, 7
(1
), pp. 1
–7
.http://www.sid.ir/en/VEWSSID/J_pdf/1000820140101.pdf24.
Litak
, G.
Borowiec
, M.
2006
, “Nonlinear Vibration of a Quarter‐Car Model Excited by the Road Surface Profile
,” Commun. Nonlinear Sci. Numer. Simul.
, 13
(7
), pp. 1373
–1383
.25.
Houfek
, M.
Sveda
, P.
Kratochvíl
, C.
2011
, “Identification of Deterministic Chaos in Dynamical Systems
,” Mechatronics
, Springer
, Berlin
.Copyright © 2018 by ASME
You do not currently have access to this content.
