Uniform Beam Dynamics Under Exponentially Moving Load on Bi-paeametric Foundation with Time-dependent Boundary Effects

Year : 2026 | Volume : 17 | Issue : 02 | Page : 53 64
By

JIMOH, A,

AJOGE, E. O,

OGUNNIGBO, O.C,

NICHOLAS, O.O,

BALOGUN, A.O,

OROGUN, O.J,

  1. Research Scholar, Department of Mathematics and Statistics, Conference University of Science and Technology, Osara, Kogi, Nigeria
  2. Research Scholar, Division of Material Science and Electronics,Centre for Energy Research and Development, Obafemi Awolowo University, Ile-Ife, Osun, Nigeria
  3. Research Scholar, Department of Robotic and Mechatronics Engineering, Federal University of Technology and Environmental Sciences, Iyin, Ekiti, Nigeria
  4. Research Scholar, Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria
  5. Research Scholar, Department of Manufacturing Industrial and Textile Engineering, Moi University, Eldoret, Nigeria
  6. Research Scholar, Materials Formation Division MetMat Engineering Limited, Lagos, Nigeria

Abstract

This study investigates the problem of a uniform elastic beam subjected to exponentially varying moving load with time dependent boundary conditions. A complex structural dynamic problem that has very significant implications for various applications such as railway systems, bridge structures, industrial machinery will be addressed in this research. A damping term is built into the uniform beam model to give a more realistic picture of the structural behaviour, while the material and geometric properties, both of which strongly affect the response amplitude, are held constant throughout the work. The supporting medium is represented as a bi-parametric foundation combining Winkler and Pasternak parameters, which together capture the normal and shear interactions between the beam and its base. The governing equations are solved through a combination of methods: the Mindlin-Goodman technique converts the non-homogeneous boundary conditions into homogeneous ones, integral Fourier series transformation reduces the resulting fourth-order partial differential equation to a second-order ordinary differential equation, and this equation is then solved using Laplace transformation together with the convolution theorem. All results are presented graphically using Maple software. It was revealed from the graphs that, as the values of the structural parameters such as Winkler foundations parameter (K), Pasternak foundation parameter (G), Axial force (N), Damping coefficient (epsilon), and load speed (v) increases, the response amplitudes of the beam decreases. The results also reveals that, the effect of Pasternak foundation parameter is more noticeable compare to that of Winkler foundation parameter. Finally, higher values of damping coefficient and load speed significantly reduces the response amplitudes of the beam there by reduces the risk of resonance effect and the safety of the occupant of the structural member will be guaranteed

Keywords: Time Dependent Boundary Conditions, Bi-Parametric Foundation, Exponentially Moving Load, Damping Coefficient, Uniform Beam, Mindlin-Goodman method.

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

How to cite this article: JIMOH, A, AJOGE, E. O, OGUNNIGBO, O.C, NICHOLAS, O.O, BALOGUN, A.O, OROGUN, O.J. Uniform Beam Dynamics Under Exponentially Moving Load on Bi-paeametric Foundation with Time-dependent Boundary Effects. Journal of Experimental & Applied Mechanics. 2026; 17(02):53-64.
How to cite this URL: JIMOH, A, AJOGE, E. O, OGUNNIGBO, O.C, NICHOLAS, O.O, BALOGUN, A.O, OROGUN, O.J. Uniform Beam Dynamics Under Exponentially Moving Load on Bi-paeametric Foundation with Time-dependent Boundary Effects. Journal of Experimental & Applied Mechanics. 2026; 17(02):53-64. Available from: https://journals.stmjournals.com/joeam/article=2026/view=253877

References

  1. Ogunlusi, T.A; Adoghe, L.O; Bala, A; Omole, E.O; Odeniyan-Fakuade, H. H & Fayose, T. S (2026): Dynamic analysis of a non-prismatic damped-cantilever beam beam resting on exponentially decaying elastic foundation under constant and harmonic distributed loads. FUDMA Journal of Sciences. Vol. 10, No. 3.
  2. Ogunlusi, T. A & Okafor, N. P (2025): Vibration and non-prismatic damped thin beam with exponentially varying thickness resting on exponentially decaying foundation under uniform distributed load. FUOYE Journal of pure and applied science. 10 (2), 92-107.
  3. Anantheswar, A; Wollny, I & Kaliske (2025): Treatment of inelastic material models within a dynamic ALE formulation for structures subjected to moving load. International Journal for Numerical methods in Engineering. Vol. 126, Issue 1.
  4. Zhang, B: Kou, Y & Jin, K (2025): Dynamic behaviour of beam with an elastic foundation under the extended moving load for electromagnetic Launch rail-structure. Journal of sound and vibration. Vol. 596, 118756.
  5. Okafor, N. P; Momoh, E. O; Ndububa, E.E & Adeshina, M. K (2025): Dynamic analysis of an exponentially decaying foundation on the response of non-uniform damped Rayleigh beam under harmonic moving load with general boundary conditions. Asian Research Journal of Mathematics, 21 (1), 35-69.
  6. Sunday, J; Omole, O. O; Ogunrinde, R. B; Kunleng, G. M; Bamisile, O. O; & Kayode, o. o (2026): Mathematical formulation of a symmetric- compact three-step algorithm for computing the spatio-temporal generalized Fitzhugh-Nagumo equation. 18 (2), 324.
  7. Arathy, M & Bennet, K (2024): Analysis of beam on elastic foundation. International Journal of creative Research thought, VOL. 12, Issue 1.
  8. Usman, M. A; Hammed, F. A & Daniel, D. O (2023): Free vibration of non-uniform double Euler- Bernoulli beam on winkler foundation using Laplace differential transform method. Journal of Engineering Science, 14 (1), 111-121.
  9. Chen, H, Ma, Q. Z & Wang, W (2024): Analytical determination of dynamic response of layered saturated frozen foundation to moving loads under plane strain conditions. Soil dynamic and Earthquake Engineering. Vol. 180, 108578.
  10. Quizizi, A; Abdoun, F & Azrar, L (2022): Non-linear dynamic of beam on non-linear fractional viscoelastic foundation subjected to moving load with variable speed. Journal of sound and vibration, 523, 116730.
  11. Pasternak, P. L (1954): On a new method of analysis of an elastic foundation by means of two foundation constant in (Russian).
  12. Olotu, O. T; Omole, E. O; Folaranmi, R. O; Yisa, B. M; Adeniran, P. O & Gbadeyan, J. A (2025): Naturally vibration analysis of axially graded tapered Rayleigh beam on quadratic bi-parametric elastic foundation. Nigerian Journal of Technology Development, Vol. 22, No 1, Pp. 79-94.
  13. Ermis, M; Kutlu, A; Omurtag, M. H (2022): Free vibration of axially FG curved beam on orthotropic Pasternak foundation via mixed finite element method. Braz. Soc. Mech. Sci. Eng. 44, 597.
  14. Lucas, O. S; Romulo, L. C & Simon, S. H (2025): Vibration Analysis of an axial loaded Euler-Bernoulli beam on two parameter foundation. 25th International Congress of Mechanical Engineering.
  15. Awodola, T. O; Awe, B. B & Jimoh, S. A (2024): Vibration of non-uniform Bernoulli- Euler beam under moving distributed masses resting on pasternak foundation subjected to variable magnitude moving load. African Journal of Mathematics and Statistics Studies. Vol. 7, Issue 1, Pp. 1-19.
  16. Ajijola, O.O (2024): Dynamic Response to moving load of prestressed damped shear beam resting on bi-parametric elastic foundation. African journal of mathematics and statistics studies. Vol. 7, Issue 4, Pp. 328-342.
  17. Jimoh, A; Ajoge, E. O& Ezeoffor, C.D (2025): Comparative Study of Clamped-Clamped and Clamped-Free Elastic Beam Resting on Bi-Parametric Subgrades and Subjected to Concentrated Moving Load. Journal of Experimental and Applied Mechanics. Vol. 16, Issue 1, Pp.17-3.3
  18. Jimoh, A; Ajoge, E. O & Olofinniyi, J.O (2025): Effects of Two Parameters Foundation on Uniform Elastic Beam Subjected to Concentrated Moving Load with Clamped-Clamped Boundary Conditions. International Journal of Mechanics and Design. Vol. 11, Issue 1, Pp.14-26.
  19. Ahmed, Y; Adam, Z; Ibrahim, E. A; Shams, A. A; Husam, E. D; Abdelgabar, A. H & Eshraga, S (2025): Viscoelastic Pasternak Foundation Analysis of a Thermoelastic Microbeam using Mpoor-Gibson-Thompson Heat Conduction under Klein-Gordon (KG) nonlocally. AIMS Mathematics, 10 (5), 10340-10358.
  20. Saurabh, K (2022): Natural Frequencies of Beams with Axial Material Graduation resting on two Parameters foundation. Trends in Sciences 19 (6): 3048.
  21. Quifeng, P; Bingqiang, Z; Chenhao, G & Xiang, L (2025): Experimental and analytical study on dynamic response of Pasternak foundation beam with local void under moving load. Soil Dynamic and Earthquake Engineering. Vol. 192, 109312.
  22. Giorgie, P; Federica, B & Pietro, S (2025): Beams on elastic foundation: A variable reduction Approach for nonlinesar contact problems. European Journal of Mechanics / A Solids 111, 105514.
  23. Mindlin, R. D and Goodman, L. E (1950): Beam Vibrations with Time Dependent Boundary Conditions, Journal of Applied Mechanics, 17, Pp. 377-380.
  24. Adedola, A (2016):Flexural Motion under moving distributed masses of beam-type structures on vlasor foundation and having time dependent boundary conditions. Ph. D Thesis, Federal University of Technology, Akure, Nigeria.
  25. Bayem, D. I; Adeloye, T. O; Adeoye, A. S (2024): Non-stationary analysis of elastically supported Rayleigh beam under the circulation of moving distributed masses on a constant sugrade to arbitrary varying time. Saudi Journal of civil engineering. 8 (10), 233-245.
  26. Jimoh, A, Ajoge, E. O, Ajiola, D. I, Oni, D. I, Abiola Kolawole, O. O, Adesanmi, O. A. (2025): Harmonically Varying Moving Load on Time Dependent Uniform Beam Resting on Pasternak Foundation. International Journal of Electro-Mechanics and Material Behavior. Vol.3, Issue 2, Pp.36-45.
  27. Jimoh, A, Ajoge, E. O, Ajiola, D. I, Nicholas, O. O, Adeyemi, S. S, Abdulkabir, L. A. (2025): Flexural Vibration of Non-Uniform Beam Resting on Bi-Parametric Foundation under Harmonic Moving Load with Non-Classical Boundary Conditions. International Journal of Mechanical Dynamics and Systems Analysis. Vol.3, Issue 2, Pp.28-41.
  28. Oni, S. T & Awodola, T (2010): Dynamic response under a moving load on an elastically supported non-prismatic Bernoulli-Euler beam on variable elastic foundation. Latin Journal of solid and structures, 3-20.
  29. Ajibola, S. O. (2009): Dynamic analysis under moving concentrated loads of Rayleigh beam with time dependent boundary conditions. Ph. D thesis, Federal University of Technology, Akure, Ondo State, Nigeria.
  30. Frybal, L (1972). Vibration of solids and structures under moving loads. Groningen; Noordhoff.
Regular Issue Subscription Original Research
Volume 17
Issue 02
Received 05/04/2026
Accepted 23/06/2026
Published 15/07/2026
Publication Time 101 Days

Login

My IP

PlumX Metrics

Support