Dynamic Response of a Rayleigh Beam Subjected to Accelerating Distributed Moving Load

Abstract

The dynamic analysis of beam structures subjected to accelerating distributed moving loads has direct applications in civil, mechanical, and transportation engineering, particularly in the design of bridges, railway tracks, and structural floors subjected to transient vehicle or machinery loads. Despite extensive research on beam dynamics, limited attention has been given to Rayleigh beams under accelerating distributed loads with considerations for shear effects and gyration radius. This study aims to investigate the dynamic response of a simply supported Rayleigh beam subjected to accelerating distributed moving loads. The governing fourth-order partial differential equation (PDE) which is based on classical Rayleigh beam theory and extends the Euler-Bernoulli formulation was formulated using standard assumptions of beam theory and then transformed through separation of variables and modal expansion. Appropriate boundary conditions were imposed, and the resulting governing system was solved numerically using the finite difference method implemented in MATLAB. Parametric studies were conducted to assess the effects of radius of gyration, shear coefficient, and shear modulus on the beam’s deflection profile. Results reveal that deflection increases significantly at the mid-span with increasing values of gyration radius (rG = 0.1, 0.2 and 0.3), shear modulus (G = 0.2, 1.2 and 2.2), and shear coefficient (K = 0.5, 1.5 and 2.5), implying reduced stiffness and higher susceptibility to dynamic amplification. The study contributes to improved predictive modeling of beam vibration under moving loads and can be applied in bridge design, railway engineering, and structural health monitoring.

Keywords

• Rayleigh Beam
• Shear Modulus
• Shear Coefficient
• Radius of Gyration
• Accelerating Load

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