Transient Response of Rayleigh Beams Transporting Moving Distributed Masses on Pasternak Foundation: Rayleigh-Ritz and Runge-Kutta Techniques

Abstract: The dynamic response of structural elements to moving loads is a fundamental problem in structural dynamics with direct relevance to civil engineering, mechanical systems, and biomechanics. This study presents a computational framework for capturing the transient behavior of Rayleigh beams' models that incorporate rotary inertia and shear deformation subjected to moving distributed masses while supported by a Pasternak (two-parameter) elastic foundation. The Pasternak model, which combines Winkler-type vertical stiffness with shear-layer interaction, increases the mathematical complexity of the governing equations. Spatial discretization is achieved via the Rayleigh–Ritz method by representing transverse deflection as a linear combination of admissible functions that satisfy clamped boundary conditions; this reduces the governing fourth-order partial differential equation to a system of second-order ordinary differential equations in time. Temporal integration is performed with the classical fourth-order Runge–Kutta (RK4) scheme to resolve the time-varying effects of the moving mass and to balance accuracy with computational efficiency. Parametric studies investigate the influence of foundation stiffness, rotary inertia, flexural rigidity and moving-mass characteristics on deflection, natural frequencies and transient amplification. Results presented as distinct, non-overlapping plots demonstrate the sensitivity of dynamic response to individual parameters and confirm the proposed method’s efficacy and adaptability for advanced modelling of engineering and biomechanical systems under dynamic loading. Keywords: Structural dynamics, Rayleigh -Ritz, Runge-Kutta, Foundation stiffness, Rotary inertia, Flexural rigidity. Title: Transient Response of Rayleigh Beams Transporting Moving Distributed Masses on Pasternak Foundation: Rayleigh-Ritz and Runge-Kutta Techniques Author: Adebola Samuel Adeoye, Tolulope Olamide Adeloye, Yahya Abdul Oluborode International Journal of Civil and Structural Engineering Research ISSN 2348-7607 (Online) Vol. 13, Issue 1, April 2025 - September 2025 Page No: 97-109 Research Publish Journals Website: www.researchpublish.com Published Date: 29-September-2025 DOI: https://doi.org/10.5281/zenodo.17224034 Paper Download Link (Source) https://www.researchpublish.com/papers/transient-response-of-rayleigh-beams-transporting-moving-distributed-masses-on-pasternak-foundation-rayleigh-ritz-and-runge-kutta-techniques