Modification of Automobile Shock Absorbers Thickness and Weight Parameters for Adaptation on Poorly Maintained Roads via Mathematical Modelling

Benard Ouma Owino; Cleophas M. Kweyu; Titus Chebion Rotich

doi:doi:10.11648/j.sdmath.20260101.12

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Modification of Automobile Shock Absorbers Thickness and Weight Parameters for Adaptation on Poorly Maintained Roads via Mathematical Modelling

Benard Ouma Owino^*, Cleophas M. Kweyu, Titus Chebion Rotich

Published in Science Discovery Mathematics (Volume 1, Issue 1)

Received: 27 August 2025 Accepted: 8 September 2025 Published: 14 February 2026

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Abstract

Uneven oscillatory forces applied to an object cause vibration, which can lead to noise, discomfort, and mechanical wear. The optimization of shock absorber thickness and weight is critical for enhancing vehicle performance on poorly maintained roads. In automobiles, vibrations due to irregular road surfaces have been mitigated using shock absorbers to enhance performance, comfort, and control. The main aim of this study was to determine the effect of automotive weights and shock absorber thickness on automobile vibrations. The objectives of this study were; to formulate a mathematical model describing the effect of automobile weight on unsteady vibrations; to generate numerical solutions of the mathematical model equations for the shock absorber modified to reduce vibrations at the mounting points; and to analyze from the numerical solution the effects of increase in velocity and weight on the automobile unsteady spring vibration. A mathematical model was developed, utilizing the central difference scheme for discretization and solved using the Jacobian iterative method, with stability conditions implemented. Through computational simulations, various thickness and weight configurations were tested under diverse road conditions. The results indicate a significant improvement in shock absorber performance, with optimized configurations that increasing shock absorber thickness reduced vibration amplitude by approximately 35%, while increased vehicle weight amplified vibrations by 20%, necessitating thicker shock absorbers for stability. Higher speeds above 80 km/h intensified unsteady vibrations on poorly maintained roads. The study concludes that modifying shock absorber thickness and optimizing weight distribution can effectively minimize automobile vibrations.

Published in	Science Discovery Mathematics (Volume 1, Issue 1)
DOI	10.11648/j.sdmath.20260101.12
Page(s)	12-18
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Vibration Damping, Shock Absorber, Automotive Weights, Shock Absorber Thickness

References

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[2]	Chen, Q., Xu, Z., Wu, M., Xiao, Y., & Shao, H. (2021). Study on dynamic characteristic analysis of vehicle shock absorbers based on bidirectional fluid–solid coupling. Engineering Applications of Computational Fluid Mechanics, 15(1), 426–436: https://doi.org/10.1080/19942060.2021.1878059
[3]	Dobre, A. (2021). Modelling the dynamic behaviour of car hydraulic dampers. 1091(1), 012018: https://doi.org/10.1088/1757-899X/1091/1/012018
[4]	Ferdek, U., & Dukała, M. (2021). Experimental analysis of nonlinear characteristics of absorbers with wire rope isolators. Open Engineering, 11(1), 1170–1179: https://doi.org/10.1515/eng-2021-0111
[5]	Goldstein, L., Ilssar, D., & Gat, A. (2020). On non-Newtonian effects in fluidic shock-absorbers. Applied Physics Letters, 117(15), 153701: https://doi.org/10.1063/5.0023938
[6]	Guan, D., Jing, X., Shen, H., Jing, L., & Gong, J. (2019). Test and simulation the failure characteristics of twin tube shock absorber. Mechanical Systems and Signal Processing, 122, 707–719: https://doi.org/10.106/j.ymssp.2018.12.052
[7]	Isermann, R. (2022). Suspension Control Systems. In Automotive Control (pp. 445–479). Springer: https://link.springer.com/chapter/10.1007/978-3-642-39440-9_15
[8]	Oude Nijhuis, M. H. (2003a). Analysis tools for the design of active structural acoustic control systems: thesis.
[9]	Potapenko, O., Gorbunov, N., Mogyla, V., Shcherbina, Y., & Hauser, V. (2019). Function Evaluation of Common and Proposed Friction Shock Absorbers for Open Box Wagon 12-7019 KRVZ. Manufacturing Technology, 19(2), 303–307: https://doi.org/10.21062/ujep/287.2019/a/1213-2489/MT/19/2/303
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[12]	Surblys, V., Žuraulis, V., & Sokolovskij, E. (2019). The influence of semi-active suspension adjustment on vehicle body pitch oscillations. Transport and Telecommunication, 20(2), 107–113. https://doi.org/10.2478/ttj-2019-0009
[13]	Tuhta, S., Günday, F., & Abrar, O. (2019). Experimental Study on Effect of Seismic Damper to Reduce the Dynamic Response of Bench Scale Steel Structure Model. İnternational Journal of Advance Research and Innovative İdeas in Education, 5(5), 901–911: https://www.researchgate.net/profile/Furkan-Guenday/publication/337758741
[14]	Wen-xue, X., & Zhen-hua, L. (2020). 3D FSI FEA simulation and analyses of the dynamic characteristics of a displacement-sensitive liquid damper. 37(9), 217–229: 217-229: https://doi.org/10.6052/j.issn.1000-4750.2019.10.0584

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APA Style

Owino, B. O., Kweyu, C. M., Rotich, T. C. (2026). Modification of Automobile Shock Absorbers Thickness and Weight Parameters for Adaptation on Poorly Maintained Roads via Mathematical Modelling. Science Discovery Mathematics, 1(1), 12-18. https://doi.org/10.11648/j.sdmath.20260101.12

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ACS Style

Owino, B. O.; Kweyu, C. M.; Rotich, T. C. Modification of Automobile Shock Absorbers Thickness and Weight Parameters for Adaptation on Poorly Maintained Roads via Mathematical Modelling. Sci. Discov. Math. 2026, 1(1), 12-18. doi: 10.11648/j.sdmath.20260101.12

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AMA Style

Owino BO, Kweyu CM, Rotich TC. Modification of Automobile Shock Absorbers Thickness and Weight Parameters for Adaptation on Poorly Maintained Roads via Mathematical Modelling. Sci Discov Math. 2026;1(1):12-18. doi: 10.11648/j.sdmath.20260101.12

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@article{10.11648/j.sdmath.20260101.12,
  author = {Benard Ouma Owino and Cleophas M. Kweyu and Titus Chebion Rotich},
  title = {Modification of Automobile Shock Absorbers Thickness and Weight Parameters for Adaptation on Poorly Maintained Roads via Mathematical Modelling},
  journal = {Science Discovery Mathematics},
  volume = {1},
  number = {1},
  pages = {12-18},
  doi = {10.11648/j.sdmath.20260101.12},
  url = {https://doi.org/10.11648/j.sdmath.20260101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sdmath.20260101.12},
  abstract = {Uneven oscillatory forces applied to an object cause vibration, which can lead to noise, discomfort, and mechanical wear. The optimization of shock absorber thickness and weight is critical for enhancing vehicle performance on poorly maintained roads. In automobiles, vibrations due to irregular road surfaces have been mitigated using shock absorbers to enhance performance, comfort, and control. The main aim of this study was to determine the effect of automotive weights and shock absorber thickness on automobile vibrations. The objectives of this study were; to formulate a mathematical model describing the effect of automobile weight on unsteady vibrations; to generate numerical solutions of the mathematical model equations for the shock absorber modified to reduce vibrations at the mounting points; and to analyze from the numerical solution the effects of increase in velocity and weight on the automobile unsteady spring vibration. A mathematical model was developed, utilizing the central difference scheme for discretization and solved using the Jacobian iterative method, with stability conditions implemented. Through computational simulations, various thickness and weight configurations were tested under diverse road conditions. The results indicate a significant improvement in shock absorber performance, with optimized configurations that increasing shock absorber thickness reduced vibration amplitude by approximately 35%, while increased vehicle weight amplified vibrations by 20%, necessitating thicker shock absorbers for stability. Higher speeds above 80 km/h intensified unsteady vibrations on poorly maintained roads. The study concludes that modifying shock absorber thickness and optimizing weight distribution can effectively minimize automobile vibrations.},
 year = {2026}
}

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TY  - JOUR
T1  - Modification of Automobile Shock Absorbers Thickness and Weight Parameters for Adaptation on Poorly Maintained Roads via Mathematical Modelling
AU  - Benard Ouma Owino
AU  - Cleophas M. Kweyu
AU  - Titus Chebion Rotich
Y1  - 2026/02/14
PY  - 2026
N1  - https://doi.org/10.11648/j.sdmath.20260101.12
DO  - 10.11648/j.sdmath.20260101.12
T2  - Science Discovery Mathematics
JF  - Science Discovery Mathematics
JO  - Science Discovery Mathematics
SP  - 12
EP  - 18
PB  - Science Publishing Group
UR  - https://doi.org/10.11648/j.sdmath.20260101.12
AB  - Uneven oscillatory forces applied to an object cause vibration, which can lead to noise, discomfort, and mechanical wear. The optimization of shock absorber thickness and weight is critical for enhancing vehicle performance on poorly maintained roads. In automobiles, vibrations due to irregular road surfaces have been mitigated using shock absorbers to enhance performance, comfort, and control. The main aim of this study was to determine the effect of automotive weights and shock absorber thickness on automobile vibrations. The objectives of this study were; to formulate a mathematical model describing the effect of automobile weight on unsteady vibrations; to generate numerical solutions of the mathematical model equations for the shock absorber modified to reduce vibrations at the mounting points; and to analyze from the numerical solution the effects of increase in velocity and weight on the automobile unsteady spring vibration. A mathematical model was developed, utilizing the central difference scheme for discretization and solved using the Jacobian iterative method, with stability conditions implemented. Through computational simulations, various thickness and weight configurations were tested under diverse road conditions. The results indicate a significant improvement in shock absorber performance, with optimized configurations that increasing shock absorber thickness reduced vibration amplitude by approximately 35%, while increased vehicle weight amplified vibrations by 20%, necessitating thicker shock absorbers for stability. Higher speeds above 80 km/h intensified unsteady vibrations on poorly maintained roads. The study concludes that modifying shock absorber thickness and optimizing weight distribution can effectively minimize automobile vibrations.
VL  - 1
IS  - 1
ER  -

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Author Information

Benard Ouma Owino

School of Science and Aerospace Studies, Department of Mathematics, Physics and Computing, Moi University, Eldoret, Kenya

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Cleophas M. Kweyu

School of Science and Aerospace Studies, Department of Mathematics, Physics and Computing, Moi University, Eldoret, Kenya
Titus Chebion Rotich

School of Science and Aerospace Studies, Department of Mathematics, Physics and Computing, Moi University, Eldoret, Kenya

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APA Style

Owino, B. O., Kweyu, C. M., Rotich, T. C. (2026). Modification of Automobile Shock Absorbers Thickness and Weight Parameters for Adaptation on Poorly Maintained Roads via Mathematical Modelling. Science Discovery Mathematics, 1(1), 12-18. https://doi.org/10.11648/j.sdmath.20260101.12

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ACS Style

Owino, B. O.; Kweyu, C. M.; Rotich, T. C. Modification of Automobile Shock Absorbers Thickness and Weight Parameters for Adaptation on Poorly Maintained Roads via Mathematical Modelling. Sci. Discov. Math. 2026, 1(1), 12-18. doi: 10.11648/j.sdmath.20260101.12

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AMA Style

Owino BO, Kweyu CM, Rotich TC. Modification of Automobile Shock Absorbers Thickness and Weight Parameters for Adaptation on Poorly Maintained Roads via Mathematical Modelling. Sci Discov Math. 2026;1(1):12-18. doi: 10.11648/j.sdmath.20260101.12

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@article{10.11648/j.sdmath.20260101.12,
  author = {Benard Ouma Owino and Cleophas M. Kweyu and Titus Chebion Rotich},
  title = {Modification of Automobile Shock Absorbers Thickness and Weight Parameters for Adaptation on Poorly Maintained Roads via Mathematical Modelling},
  journal = {Science Discovery Mathematics},
  volume = {1},
  number = {1},
  pages = {12-18},
  doi = {10.11648/j.sdmath.20260101.12},
  url = {https://doi.org/10.11648/j.sdmath.20260101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sdmath.20260101.12},
  abstract = {Uneven oscillatory forces applied to an object cause vibration, which can lead to noise, discomfort, and mechanical wear. The optimization of shock absorber thickness and weight is critical for enhancing vehicle performance on poorly maintained roads. In automobiles, vibrations due to irregular road surfaces have been mitigated using shock absorbers to enhance performance, comfort, and control. The main aim of this study was to determine the effect of automotive weights and shock absorber thickness on automobile vibrations. The objectives of this study were; to formulate a mathematical model describing the effect of automobile weight on unsteady vibrations; to generate numerical solutions of the mathematical model equations for the shock absorber modified to reduce vibrations at the mounting points; and to analyze from the numerical solution the effects of increase in velocity and weight on the automobile unsteady spring vibration. A mathematical model was developed, utilizing the central difference scheme for discretization and solved using the Jacobian iterative method, with stability conditions implemented. Through computational simulations, various thickness and weight configurations were tested under diverse road conditions. The results indicate a significant improvement in shock absorber performance, with optimized configurations that increasing shock absorber thickness reduced vibration amplitude by approximately 35%, while increased vehicle weight amplified vibrations by 20%, necessitating thicker shock absorbers for stability. Higher speeds above 80 km/h intensified unsteady vibrations on poorly maintained roads. The study concludes that modifying shock absorber thickness and optimizing weight distribution can effectively minimize automobile vibrations.},
 year = {2026}
}

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TY  - JOUR
T1  - Modification of Automobile Shock Absorbers Thickness and Weight Parameters for Adaptation on Poorly Maintained Roads via Mathematical Modelling
AU  - Benard Ouma Owino
AU  - Cleophas M. Kweyu
AU  - Titus Chebion Rotich
Y1  - 2026/02/14
PY  - 2026
N1  - https://doi.org/10.11648/j.sdmath.20260101.12
DO  - 10.11648/j.sdmath.20260101.12
T2  - Science Discovery Mathematics
JF  - Science Discovery Mathematics
JO  - Science Discovery Mathematics
SP  - 12
EP  - 18
PB  - Science Publishing Group
UR  - https://doi.org/10.11648/j.sdmath.20260101.12
AB  - Uneven oscillatory forces applied to an object cause vibration, which can lead to noise, discomfort, and mechanical wear. The optimization of shock absorber thickness and weight is critical for enhancing vehicle performance on poorly maintained roads. In automobiles, vibrations due to irregular road surfaces have been mitigated using shock absorbers to enhance performance, comfort, and control. The main aim of this study was to determine the effect of automotive weights and shock absorber thickness on automobile vibrations. The objectives of this study were; to formulate a mathematical model describing the effect of automobile weight on unsteady vibrations; to generate numerical solutions of the mathematical model equations for the shock absorber modified to reduce vibrations at the mounting points; and to analyze from the numerical solution the effects of increase in velocity and weight on the automobile unsteady spring vibration. A mathematical model was developed, utilizing the central difference scheme for discretization and solved using the Jacobian iterative method, with stability conditions implemented. Through computational simulations, various thickness and weight configurations were tested under diverse road conditions. The results indicate a significant improvement in shock absorber performance, with optimized configurations that increasing shock absorber thickness reduced vibration amplitude by approximately 35%, while increased vehicle weight amplified vibrations by 20%, necessitating thicker shock absorbers for stability. Higher speeds above 80 km/h intensified unsteady vibrations on poorly maintained roads. The study concludes that modifying shock absorber thickness and optimizing weight distribution can effectively minimize automobile vibrations.
VL  - 1
IS  - 1
ER  -

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