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Jun 19, 2026Keywords:
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Main Article Content
Natural vibration analysis of axially graded tapered rayleigh beams on a quadratic bi-parametric elastic foundation
Abstract
Understanding the dynamic behaviour of non-homogeneous beams on elastic foundations is vital for ensuring the stability and safety of engineering structures such as bridges, buildings, and mechanical systems. This study aims to address this problem by investigating the natural vibration characteristics of such beams. The mechanical properties of the beam and the foundation stiffness are assumed to vary along the longitudinal direction. Two boundary conditions-clamped-free and clamped-clamped are considered. The differential transform method (DTM) is employed to solve the governing equation of motion, providing a numerical approximation of the beam's dynamic behaviour. The results, presented in both tabular and graphical formats, highlight the influence of key parameters such as the inverse of the slenderness ratio, foundation stiffness, and boundary conditions on the free vibration response. The findings indicate that increasing foundation stiffness leads to higher natural frequencies, with the Pasternak foundation yielding the highest values. Additionally, an axially functionally graded Rayleigh beam on a Pasternak foundation exhibits superior natural frequencies compared to a similar beam on a Winkler foundation. The effectiveness and accuracy of the DTM are further validated through two illustrative dynamic response problems, with results demonstrating excellent agreement with existing literature.
