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Phase Plane Stability of Damping Regimes in a Vehicle Suspension System

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Author Affiliations

  • 1Department of Mathematics, Nrupathunga University, Bengaluru, India
  • 2Department of Mathematics, Nrupathunga University, Bengaluru, India

Res. J. Mathematical & Statistical Sci., Volume 14, Issue (3), Pages 10-13, September,12 (2026)

Abstract

This study looks at phase plane portraits of vehicle suspension dynamics. It creates three distinct trajectory patterns: spiral, straight radial, and curved. These patterns reflect important suspension behaviors in different types of vehicles. These mathematical patterns directly inform real driving experiences. Spiral trajectories, common in sports cars, provide quick handling for fast turns and better road feel. Straight radial trajectories, typical of family sedans, provide balanced performance and quick stabilization after road disturbances, making them perfect for daily driving. Curved trajectories in trucks and luxury vehicles help them respond smoothly to uneven surfaces. This design ensures comfort and stability, especially during long drives or when carrying heavy loads. The research gives engineers, mechanics, and manufacturers visual tools. They can use these tools to check suspension features and pick the right shock absorber setups. Linking trajectory shapes to vehicle performance needs to optimize tuning, boosts safety, and cut down component wear. Engineers like math validation. Mechanics benefit from intuitive diagnostic guides. Manufacturers gain better design efficiency. This work combines theory with real-world car applications. It helps design better suspension systems for specific vehicle functions and driving conditions.

References

  1. Wong. J. Y (2008)., Theory of Ground Vehicles, 4th ed., Wiley., undefined
  2. Rao S. S, (2017)., Mechanical Vibrations, 6th ed., Pearson., undefined
  3. Gillespie, T. D. (1992)., Fundamentals of Vehicle Dynamics., SAE International.
  4. Inman, D. J. (2014)., Engineering Vibration (4th ed.)., Pearson,
  5. Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P. (2007)., Numerical Recipes: The Art of Scientific Computing (3rd ed.)., Cambridge University Press.
  6. Blundell, M. and Harty, D. (2004)., The Multibody Systems Approach to Vehicle Dynamics (2nd ed.)., Butterworth Heinemann.
  7. Sharp, R. S. (2009)., Vehicle dynamics., Proceedings of the Institution of Mechanical Engineers, 223, 305–322.
  8. Sprott, J. C. (2005)., Phase portraits of damped oscillators., Chaos, 15(2), 110-118.
  9. Bobier, C. G. (2012)., Phase portrait approach to vehicle stabilization (Ph.D. dissertation)., Stanford University.
  10. Molla, M., et al. (2024)., Nonlinearity in quarter car models., Scientific Reports, 14, 102-112.
  11. Barethiye, S., et al. (2017)., Nonlinear suspension dynamics., International Journal of Applied Mechanics and Engineering, 22, 45-56.
  12. SciPy Development Team (2024)., SciPy: Scientific computing tools for Python.,
  13. Sharma, S. K., Sharma, R. C., Mohapatra, S., Fouly, A., Hossain, I., & Lee, J. (2024)., Technological advancements in oscillation reduction for propulsion shaft systems., Journal of Vibration Engineering & Technologies, 12(Suppl 2), 1779-1797.
  14. Ren, Y., & Zhou, L. (2025)., Stability and Hopf bifurcation analysis of a nonlinear active suspension system with time-delay., International Journal of Bifurcation and Chaos, 35(15), 2550169.
  15. Shelke, G. D., Mitra, A. C., & Varude, V. R. (2018)., Validation of simulation and analytical model of nonlinear passive vehicle suspension system for quarter car., Materials Today: Proceedings, 5(9), 19294-19302.
  16. Aye, Y. Y., Win, H. H., Min Swe, W. W., & Lat, A. K. (2024)., Vibration Analysis of Suspension System for 3DOF Quarter Car Model with Tire Damping., International Journal of Mechanical Engineering and Robotics Research, 13(2), 196–204.
  17. Awad, S., Awad, E. O., Ata, W. G., El-Demerdash, S. M., & Gad, A. S. (2024)., Experimental evaluation of damping and stiffness in optimized active sport utility vehicle suspension systems., International Journal of Automotive and Mechanical Engineering, 21(3), 11469-11485.
  18. Howard, G., Whitehead, J. P., & Bastow, D. (2004)., Car suspension and handling.,
  19. IEEE. (2023)., RK4 stability in suspension control., IEEE Transactions on Vehicle Technology, 72, 1420-1432.
  20. ChassisSim. (2023)., Damper selection guide (ChassisSim Technical Report)., chassis-sim.com. https://www.chassis-sim.com/