Comparative Study of Uniform and Non-Uniform Beams Resting on Bi-Parametric Foundation Under Harmonic Load with Time Dependent Boundary Conditions

Year : 2026 | Volume : 04 | Issue : 01 | Page : 33 50
    By

    Jimoh A.*,

  • Ajoge E.O.,

  • Ajiola D.I.,

  • Eluyemi A.A.,

  • Balogun A.O.,

  • Orogun O.J.,

  1. Research Scholar,, Department of Mathematics and Statistics, Conference University of Science and Technology, Osara, Kogi State, Nigeria
  2. Research Scholar, Centre for Energy Research and Development, Obafemi Awolowo University, Ile-Ife, Osun, State, Nigeria
  3. Research Scholar, Department of Biochemistry, Chemistry, and Physics. College of Science and Mathematics, Georgia Southern University, 1332 Southern Drive Statesboro, GA 30458, USA
  4. Research Scholar, Centre for Energy Research and Development, Obafemi Awolowo University, Ile-Ife, Osun, State, Nigeria
  5. Research Scholar, Department of Manufacturing Industrial and Textile Engineering, Moi University, Eldoret, Kenya.
  6. Research Scholar, Metmat Engineering Limited, Lagos, Nigeria

Abstract

In this study, we investigated uniform and non-uniform damped and time-dependent elastic beams resting on bi-parametric foundation subjected to harmonically varying moving load. The beam properties, including moment of inertia and mass per unit length, were assumed to be either constant or varying with position along the beam span in this study. The solution methods were based on Mindlin-Goodman method, Fourier sine transformation, weighted residual method, integral transformation, and theory of convolution. The response amplitudes of the beams were calculated by considering the structural parameters in the models equations with the aid of Maple software and results were presented graphically. It is seen from graphs that, as values of the damping coefficient and axial force increases, the response amplitudes of both uniform and non-uniform beams decrease. Also, decreases in deflection profiles of both uniform and non-uniform beams were brought about as a result of increases in foundation modulus and shear modulus. Increases in the values of load natural frequency and velocity of the moving load lead to decreases in the response amplitude of uniform and non-uniform beams. The findings also revealed that, in each effect of the structural parameters considered, it is seen that, the deflection profiles of the uniform beam is significantly higher than the non-uniform beam, that is, for constant values of all the structural parameters, the response amplitudes of uniform beam is much higher than that of non-uniform beam and as a result, resonance effect reach earlier in the uniform beam than the non-uniform beam. The uniform beam that produces higher deflection profiles than the non-uniform beam was attributed to properties of the beam, while it is constant in the case of uniform beam, its varies in the non-uniform beam. Finally, the effects of load velocity, load natural frequency and damping coefficient on the dynamical system are more noticeable compared to other structural parameters. To reduce the resonance effect which can result in stability of the dynamical system and guarantee the safety of lives, all those factors that can significantly reduce vibrations of the beam subjected to moving load should be properly taken into consideration by designers of such structural members during the designing and implementation stage.

Keywords: Bi-parametric foundation, Damped beam, Harmonically varying moving load, Time dependent boundary conditions, Uniform, and non-uniform beam.

[This article belongs to International Journal of Mechanical Dynamics and Systems Analysis ]

How to cite this article:
Jimoh A.*, Ajoge E.O., Ajiola D.I., Eluyemi A.A., Balogun A.O., Orogun O.J.. Comparative Study of Uniform and Non-Uniform Beams Resting on Bi-Parametric Foundation Under Harmonic Load with Time Dependent Boundary Conditions. International Journal of Mechanical Dynamics and Systems Analysis. 2026; 04(01):33-50.
How to cite this URL:
Jimoh A.*, Ajoge E.O., Ajiola D.I., Eluyemi A.A., Balogun A.O., Orogun O.J.. Comparative Study of Uniform and Non-Uniform Beams Resting on Bi-Parametric Foundation Under Harmonic Load with Time Dependent Boundary Conditions. International Journal of Mechanical Dynamics and Systems Analysis. 2026; 04(01):33-50. Available from: https://journals.stmjournals.com/ijmdsa/article=2026/view=244890


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Regular Issue Subscription Original Research
Volume 04
Issue 01
Received 12/03/2026
Accepted 13/03/2026
Published 25/03/2026
Publication Time 13 Days
1

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