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Mathematical Methodology: Incremental Harmonic Balance Method and its Application in Automotive Crashes
Technical Paper
2007-01-2140
ISSN: 0148-7191, e-ISSN: 2688-3627
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English
Abstract
The work carried out in this paper includes developing and analyzing mathematical models of vehicle structures involved in head-on collisions with different obstacles. Crash analysis of vehicle-to-vehicle and vehicle-to-rigid fixed barrier in full and offset collision events is presented using a mathematical methodology and dynamic responses are obtained with the aid of an analytical approach using Incremental Harmonic Balance Method (IHBM). Moreover, optimized vehicle structures with additional energy absorbers are presented and analyzed. The rail deformation and occupant deceleration are used for interpreting the results. It is proven from numerical simulations that development and analysis of mathematical models are efficient tools for estimating the dynamic response for different frontal collision events. It is also shown that mathematical models are flexible and useful in optimization studies. Furthermore, it is shown that IHBM is an effective method to solve dynamic problems, with strong nonlinear stiffness and dampening characteristics, effectively and accurately. It is also proven that significant improvements to both deformation and deceleration injuries are obtained and crash severity are minimized using optimized vehicle structures.
Authors
Citation
Elmarakbi, A., "Mathematical Methodology: Incremental Harmonic Balance Method and its Application in Automotive Crashes," SAE Technical Paper 2007-01-2140, 2007, https://doi.org/10.4271/2007-01-2140.Also In
SAE 2007 Transactions Journal of Passenger Cars: Mechanical Systems
Number: V116-6; Published: 2008-08-15
Number: V116-6; Published: 2008-08-15
References
- Coo P. Janssen E. Goudswaard A. Wismans J. Rashidy M. “Simulation Model for Vehicle Performance Improvement in Lateral Collision” Paper No. 91-S5-O-25, 13 th ESV Conference Paris, France 1991
- Kamal M. “Analysis and Simulation of Vehicle-to-Barrier Impact” SAE Paper No. 700414 , SAE Transactions 79 1498 1503 1970
- Bennett J. Lust R. Wang J. “Optimal Design Strategies in Crashworthiness and Occupant Protection” The ASME Mechanical Engineering Congress and Exposition, ASME New York, USA 51 66 1991
- Hollowell W. “Adaptive Time Domain, Constrained System Identification of Nonlinear Structure” Symposium on Vehicle Crashworthiness Including Impact Biomecanics, ASME 105 123 1986
- Mahmood H. Wheatly D. El-Bkaily M. Bakkar J. “On The Front End Design of Automotive Vehicle for Crashworthiness” The ASME Mechanical Engineering Congress and Exposition, ASME New York, USA 311 318 1993
- Mahmood H. Li C. “Front End Design of Vehicle Structure Subjected to Frontal Crash Load” The ASME Mechanical Engineering Congress and Exposition, ASME Dallas, Texas, USA 233 240 1997
- Mooi H. Hubers J. “Simple and Effective Lumped Mass Models for Determining Kinetics and Dynamics of Vehicle-to-Vehicle Crashes” 1 st International Crashworthiness Conference Dearborn, Michigan, USA 28 41 1998
- Fileta B. Liu X. “Predicting Vehicle Crash Proficient in Offset Barrier Impact” The ASME Mechanical Engineering Congress and Exposition, ASME New York, USA 1 23 1996
- Elsholz J. “Relationship Between Vehicle Front-End Deformation and Efficiency of Safety Belts During Frontal Impact” 5 th ESV Conference London, England 674 681 1974
- Lau S. Cheuhng Y. Wu S. “A variable Parameter Incrementation Method for Dynamic Instability of Linear and Nonlinear Elastic Systems” Journal of Applied Mechanics 49 849 853 1982
- Lau S. Cheuhng Y. Wu S. “Incremental Harmonic Balance Method with Multiple Time Scales for Periodic Vibration of Nonlinear systems” Journal of Applied Mechanics 50 871 876 1983
- Lau S. Cheuhng Y. Wu S. “Nonlinear Vibration of Thin Elastic Plates” Journal of Applied Mechanics 51 845 851 1984
- Lau S. Cheuhng Y. Chen S. “An Alternative Perturbation Procedure of Multiple Scales for Nonlinear Dynamics Systems” Journal of Applied Mechanics 56 667 675 1989
- Lau S. Zhang W. “Nonlinear Vibrations of Piecewise Linear Systems by Incremental Harmonic Balance Method” Journal of Applied Mechanics 59 153 160 1992
- Lau S. Yuen S. “Solution Diagram of Nonlinear Dynamic Systems by IHB method” Journal of Sound and Vibration 167 303 316 1993
- Pun D. Liu Y. “On the Design of the Piecewise Linear Vibration absorber” Journal of Nonlinear Dynamics 22 393 413 2000
- Chen S. Cheung Y. Xing H. “Nonlinear vibration of Plane Structures by Finite Element and Incremental Harmonic Balance Method” Journal of Nonlinear Dynamics 26 87 104 2001
- Schwarz R. “Hydraulic Energy Absorption Systems for High-Energy Collisions” 2 nd ESV Conference, Sindelfingen Germany 36 74 1971
- Appel H. Tomasd J. “The Energy Management Structure for the Volkswagen ESV” SAE Paper No. 730078
- Rupp W. “Front Energy Management Parametric Variation Study” 5th ESV Conference London, England 602 614 1974
- Jawad S. Mahmood H. Baccouch M. “Smart Structure For Improving Crashworthiness in Vehicle Frontal Collisions” The ASME Mechanical Engineering Congress and Exposition, ASME, Nashville Tennessee, USA 135 144 1999
- Witteman W. Kriens R. “Modeling of An Innovative Frontal Car Structure: Similar Deceleration Curves at Full Overlap, 40 Percent Offset and 30 Degrees collisions” 16 th ESV Conference Windsor, Ontario, Canada 194 212 1998
- Witteman W. Kriens R. “The necessity of an Adaptive Vehicle Structure to Optimize Deceleration Pulses for Different Crash Velocities” 17 th ESV Conference Amsterdam, The Netherlands 1 10 2001
- Ellis E. “Extensible Vehicle Bumper” Pat No. 3947061, US Patent Office 1976
- Reuber G. Braun A. “Bumper System Having An Extendable Bumper For Automotive Vehicles” Pat No. 5370429, US Patent Office 1994
- Wang J. “Bumper Energy Absorber” Pat No. 5967573, US Patent Office 1999
- Namuduri G. Peruski L. Jones G. “Extendable Bumper System and Method of Control” Pat No. 6709035, US Patent Office 2004
- Cacciaube A. “Frontal Crash-Influence of the Deceleration Mode (at the Seat Belts Anchorage Points) on Severity Indices” 3 rd ESV Conference Washington, USA 141 145 1972