FLEXURAL VIBRATION OF NON-UNIFORM BEAM ON BI-PARAMETRIC FOUNDATION UNDER HARMONIC MOVING LOAD WITH NON-CLASSICAL BOUNDARY CONDITIONS

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Year : 2025 | Volume : 3 | 02 | Page :
    By

    JIMOH, A.,

  • AJOGE, E. O.,

  • AJIOLA, D. I,

  • NICHOLAS, O. O.,

  • ADEYEMI, S. S.,

  • ABDULKABIR, L. A.,

  1. Research Professor, Department of Mathematics and Statistics, Conference University of Science and Technology, Osara, Kogi State, Nigeria
  2. Research Scholar, Department of 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, Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria
  5. Research Scholar, Department of Mechanical and Materials Engineering, University of Turku, , Finland
  6. Research Scholar, Department of Material Science and Engineering, Obafemi Awolowo University, Ile-Ife, , Nigeria

Abstract

The dynamic response to harmonically varying moving loads of non-uniform elastic beam resting on bi-parametric foundation with non-classical boundary condition, time dependent in particular is examined in this paper. Here, the beam is considered non-uniform, with the moment of inertia and the distributed mass varying continuously along the span L as functions of the position 𝑥. In order to guarantee a more stable structure and a reduce risk of resonance, the damping term is incorporated into the governing partial differential equations that describes the dynamical system. The effects of other structural parameters such as foundation stiffness (K), shear modulus (G), axial force (N), Load natural frequency (W), and load velocity (C) are also taken into consideration. The solutions are obtained by using Mindlin Goodman method, Galerkin method, Laplace integral transformation and theory of convolution. Maple software was used to calculate the response amplitudes and presented graphically. The plots clearly show that as the damping coefficient increases, the corresponding deflection of the beam subjected to harmonic moving loading diminishes substantially. It was also noted that the deflection profiles decreases as foundation stiffness and shear modulus increases. It was also discovered that as axial force, load natural frequency, and velocity of the moving load increases, the deflection profiles decreases. The findings also revealed that, the load natural frequency and damping coefficient have more significant effects on the structure subjected to harmonically varying moving load compared with other structural parameters. Hence, in order to reduce the adverse effects of resonance and guarantee the safety of lives and properties, higher values of those parameters are recommended for the designers of such structures.

Keywords: Non-uniform beam, time dependent boundary conditions, Harmonic moving load, Bi-Parametric Foundation, Damping Coefficient

How to cite this article:
JIMOH, A., AJOGE, E. O., AJIOLA, D. I, NICHOLAS, O. O., ADEYEMI, S. S., ABDULKABIR, L. A.. FLEXURAL VIBRATION OF NON-UNIFORM BEAM ON BI-PARAMETRIC FOUNDATION UNDER HARMONIC MOVING LOAD WITH NON-CLASSICAL BOUNDARY CONDITIONS. International Journal of Mechanical Dynamics and Systems Analysis. 2025; 03(02):-.
How to cite this URL:
JIMOH, A., AJOGE, E. O., AJIOLA, D. I, NICHOLAS, O. O., ADEYEMI, S. S., ABDULKABIR, L. A.. FLEXURAL VIBRATION OF NON-UNIFORM BEAM ON BI-PARAMETRIC FOUNDATION UNDER HARMONIC MOVING LOAD WITH NON-CLASSICAL BOUNDARY CONDITIONS. International Journal of Mechanical Dynamics and Systems Analysis. 2025; 03(02):-. Available from: https://journals.stmjournals.com/ijmdsa/article=2025/view=234142


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Ahead of Print Subscription Review Article
Volume 03
02
Received 30/10/2025
Accepted 31/10/2025
Published 12/12/2025
Publication Time 43 Days
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