Analysis of Simply Supported and Clamped-Clamped Beam Resting on a Pasternak Foundation Subjected to Moving Load with a Damping Term

Year : 2025 | Volume : 16 | Issue : 03 | Page : 42 59
    By

    Atiti S. Ehidiame,

  • Momoh S. Omeiza,

  • Edogbanya O. Helen,

  • Gyegwe M. Jessica,

  1. Research Scholar, Department of Mathematics, Federal University Lokoja, Kogi, Nigeria
  2. Research Scholar, Department of Mathematics, Federal University Lokoja, Kogi, Nigeria
  3. Research Scholar, Department of Mathematics, Federal University Lokoja, Kogi, Nigeria
  4. Research Scholar, Department of Mathematics, Federal University Lokoja, Kogi, Nigeria

Abstract

A comparative analysis of simply supported and clamped-clamped Bernoulli-Euler beams resting on a Pasternak foundation under the action of a concentrated moving load with a damping term, when the inertia effect of the moving load is considered in its analysis, was investigated in this study. The governing equation was solved by representing the Dirac delta function through a Fourier cosine series and applying a combination of analytical techniques, including the generalized finite integral transform, Struble’s asymptotic method, and the Laplace transform. The resulting solutions were then evaluated under both simply supported and clamped-clamped boundary conditions to determine the beam’s dynamic response. In both cases, the plotted results revealed that the amplitude of vibration decreases progressively as the damping coefficient, shear modulus, foundation stiffness, and axial load parameters increase. However, the deflection profiles of the simply supported beam are generally higher for the moving force problem. In addition, the damping term had a far higher effect on the beam’s deflection for the moving force case when compared with other parameters. Also, the moving force problem is not a safe approximation for the moving mass problem. These findings are in agreement with those in literature. Furthermore, the clamped-clamped condition had deflections to the far right, while that of the simply supported condition was typically at the midpoint of the graph. Thus, the beam’s safety and longevity are ensured when the values of each parameter increase, and the introduction of the damping term will ensure safety over other parameters.

Keywords: Beam, clamped-clamped support, damping, simply supported, Pasternak foundation

[This article belongs to Journal of Experimental & Applied Mechanics ]

How to cite this article:
Atiti S. Ehidiame, Momoh S. Omeiza, Edogbanya O. Helen, Gyegwe M. Jessica. Analysis of Simply Supported and Clamped-Clamped Beam Resting on a Pasternak Foundation Subjected to Moving Load with a Damping Term. Journal of Experimental & Applied Mechanics. 2025; 16(03):42-59.
How to cite this URL:
Atiti S. Ehidiame, Momoh S. Omeiza, Edogbanya O. Helen, Gyegwe M. Jessica. Analysis of Simply Supported and Clamped-Clamped Beam Resting on a Pasternak Foundation Subjected to Moving Load with a Damping Term. Journal of Experimental & Applied Mechanics. 2025; 16(03):42-59. Available from: https://journals.stmjournals.com/joeam/article=2025/view=234633


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Regular Issue Subscription Review Article
Volume 16
Issue 03
Received 26/08/2025
Accepted 10/09/2025
Published 17/10/2025
Publication Time 52 Days
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