Impact Dynamics Models: a Short Review on Nonlinearities Effects
(*) Corresponding author
DOI: https://doi.org/10.15866/ireme.v11i3.11035
Abstract
Impact is a phenomenon present in a great number of situations, and in some of them, there is a need to know the properties of the impact on the bodies that collide. In that sense, this paper presents an impact model that represents a vehicle collision where the phenomenon is modeled as a spring-mass system. In order to establish a model that can properly represent the phenomenon, the spring and the damper of the system were considered to have linear and nonlinear characteristic, so that the system that best represents the phenomenon could be evaluated by comparing its responses with an experimental signal obtained in the literature. Also, the fractional theory was used in order to check its suitability to describe the phenomenon. The paper presents four cases: a linear system, a system with a spring with a cubic force-deflection behavior, a damper with a fractional damping order and a spring with elasto-plastic characteristic.
Copyright © 2017 Praise Worthy Prize - All rights reserved.
Keywords
Full Text:
PDFReferences
Gharib, M., & Hurmuzlu, Y. (2012). A new contact force model for low coefficient of restitution impact. Journal of Applied Mechanics, 79(6), 064506.
http://dx.doi.org/10.1115/1.4006494
Ahmad, M.; Ismail, K. A.; Mat, F. Impact Models And Coefficient of Restitution: A Review. ARPN Journal of Engineering and Applied Sciences, 11(10), 6549-6555, 2016.
http://dx.doi.org/10.4028/www.scientific.net/kem.715.180
Gilardi, G., & Sharf, I. (2002). Literature survey of contact dynamics modelling. Mechanism and Machine Theory, 37(10), 1213–1239, 2002.
http://dx.doi.org/10.1016/s0094-114x(02)00045-9
WEIR, Graham; TALLON, Stephen. The coefficient of restitution for normal incident, low velocity particle impacts. Chemical Engineering Science, v. 60, n. 13, p. 3637-3647, 2005.
http://dx.doi.org/10.1016/j.ces.2005.01.040
Klausen, Andreas, et al. "Firefly optimization and mathematical modeling of a vehicle crash test based on single-mass." Journal of Applied Mathematics, 2014 (2014).
http://dx.doi.org/10.1155/2014/150319
Zaouk AK, Bedewi NE, Kan CD and Marzougui D. Validation of a non-linear finite element vehicle model using multiple impact data. ASME Applied Mechanics Division publications-AMD 1996; 218, 91-106.
http://dx.doi.org/10.1533/cras.2000.0121
Jeyakumar, P., Devaradjane, G., Energy Absorption by Square, Circular, Pentagon and Hexagonal Steel Tubes Under Impact Loading for Automotive Crush Box Applications, (2013) International Review of Mechanical Engineering (IREME), 7 (7), pp. 1421-1426.
G. Sun, F. Xu, G. Li, and Q. Li, “Crashing analysis and multiobjective optimization for thin-walled structures with functionally graded thickness,” International Journal of Impact Engineering, vol. 64, pp. 62–74, 2014.
http://dx.doi.org/10.1016/j.ijimpeng.2013.10.004
Y. Peng, J. Yang, C. Deck, and R. Willinger, “Finite element modeling of crash test behavior for windshield laminated glass,” International Journal of Impact Engineering, vol. 57, pp. 27–35, 2013.
http://dx.doi.org/10.1016/j.ijimpeng.2013.01.010
Niu Y, Shen W, Stuhmiller JH (2007) Finite element models of rib as an inhomogeneous beam structure under high-speed impacts. Med Eng Phys 29(7):788–798.
http://dx.doi.org/10.1016/j.medengphy.2006.08.015
Pawlus W, Nielsen JE, Karimi HR, Robbersmyr KG.Mathematical modeling and analysis of a vehicle crash. In: The 4th European computing conference, Stevens Point,Wis, USA, April 2010, pp. 194–199.
http://dx.doi.org/10.2478/s13531-012-0055-8
Pawlus W, Nielsen JE, Karimi HR, Robbersmyr KG.Development of mathematical models for analysis of a vehicle crash. WSEAS Trans Appl Theor Mech 2010;5:156-165.
http://dx.doi.org/10.1109/isscaa.2010.5634041
Pawlus W, Nielsen JE, Karimi HR, Robbersmyr KG. Furtherresults on mathematical models of vehicle localized impact. In: The 3rd international symposium on systems and control in aeronautics and astronautics, Harbin, China June 2010,p. 1047-1052.
http://dx.doi.org/10.1109/isscaa.2010.5634041
X. Yang and X. He, “Firefly algorithm: recent advances and applications,” International Journal of Swarm Intelligence, vol. 1, pp. 36–50, 2013.
http://dx.doi.org/10.1504/ijsi.2013.055801
L. Guo and G. Wang, “A novel hybrid bat algorithm with harmony search for global numerical optimization,” Journal of Applied Mathematics, vol. 2013, Article ID 696491, 21 pages, 2013.
http://dx.doi.org/10.1155/2013/696491
L. Tang, H. Wang, G. Li, and F. Xu, “Adaptive heuristic search algorithm for discrete variables based multi-objective optimization,” Structural and Multidisciplinary Optimization, vol. 48, no. 4, pp. 821–836, 2013.
http://dx.doi.org/10.1007/s00158-013-0932-7
Giavotto V, Puccinelli L, Borri M, Edelman A, Heijer T (1983) Vehicle dynamics and crash dynamics with minicomputer. Comput Struct 16(1):381–393.
http://dx.doi.org/10.1016/0045-7949(83)90177-3
Harmati IA, Rovid A, Szeidl L, Varlaki P (2008) Energy distribution modeling of car body deformation using LPV representations and fuzzy reasoning. WSEAS Trans Syst 7(1):1228–1237.
http://dx.doi.org/10.1109/ines.2006.1689349
Omar T, Eskandarian A, Bedewi N (1998) Vehicle crash modelling using recurrent neural networks. Math ComputModel 28(9):31–42.
http://dx.doi.org/10.1016/s0895-7177(98)00143-5
Pawlus W, Nielsen JE, Karimi HR, Robbersmyr KG (2010) Comparative analysis of vehicle to pole collision models established using analytical methods and neural networks. In: The 5th IET international system safety conference, Manchester, UK.
http://dx.doi.org/10.1049/cp.2010.0817
Várkonyi-Kóczy AR, Rövid A, Várlaki P (2004) Intelligent methods for car deformation modeling and crash speed estimation. In: The 1st Romanian–Hungarian joint symposium on applied computational intelligence, Timisoara, Romania.
http://dx.doi.org/10.1109/icons.2007.32
M. Huang, Vehicle crash mechanics (CRC Press, Boca Raton, 2002), 1st ed.
http://dx.doi.org/10.1002/amo.860040608
Petráš, I.. Modeling and numerical analysis of fractional-order Bloch equations. Computers and Mathematics with Applications 61, p. 341-356, 2011.
http://dx.doi.org/10.1016/j.camwa.2010.11.009
Jia, J., Shen, X., and Hua, H., 2007, “Viscoelastic Behavior Analysis and Application of the Fractional Derivative Maxwell Model,” J. Vib. Control, 13(4), pp. 385–401.
http://dx.doi.org/10.1177/1077546307076284
Shokooh, A., and Suarez, L., 1999, “A Comparison of Numerical Methods Applied to a Fractional Model of Damping Materials,” J. Vib. Control, 5, pp. 331–354.
http://dx.doi.org/10.1177/107754639900500301
Sorrentino, S., and Fasana, A., 2007, “Finite Element Analysis of Vibrating Linear Systems With Fractional Derivative Viscoelastic Models,” J. Sound Vib. 299, pp. 839–853.
http://dx.doi.org/10.1016/j.jsv.2006.07.027
CAO, Junyi et al. Nonlinear dynamics of duffing system with fractional order damping. Journal of Computational and Nonlinear Dynamics, v. 5, n. 4, p. 041012, 2010.
http://dx.doi.org/10.1115/1.4002092
Pawlus W, Karimi HR and Robbersmyr KG. Mathematical modeling of a vehicle crash test based on elasto-plastic unloading scenarios of spring-mass models. The International Journal of Advanced Manufacturing Technology 2011; 55: 369-378.
http://dx.doi.org/10.1007/s00170-010-3056-x
W. Pawlus, H. R. Karimi, and K. G. Robbersmyr, “Investigation of vehicle crash modeling techniques: theory and application,” The International Journal of Advanced Manufacturing Technology, vol. 70, no. 5–8, pp. 965–993, 2014.
http://dx.doi.org/10.1007/s00170-013-5320-3
Refbacks
- There are currently no refbacks.
Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize