Calculation of the Buckling Load Factor of a Non-Prismatic Beam on a Winkler-Pasternak Foundation under Axial Harmonic Loading

Purpose This study aims to analyze the dynamic stability of non-prismatic beams resting on a Winkler-Pasternak foundation under axial harmonic loading. The objective is to evaluate the influence of geometric tapering and foundation stiffness parameters on the buckling behavior in both static and dynamic conditions. Design/methodology/approach The governing equations are derived using Hamilton's principle. The Rayleigh-Ritz numerical method with Chebyshev polynomials is applied to approximate the displacement function. The weak form is used to extract stiffness and mass matrices. Dynamic responses are analyzed using the Bolotin method and solved via MATLAB programming. Findings An increase in the tapering ratio reduces the beam's flexural rigidity, lowering the resonance frequency. Meanwhile, higher Winkler and Pasternak coefficients raise the system's stiffness and shift the resonance frequency. Pasternak shear modulus has a stronger influence on dynamic stability due to its second-order derivative dependence. Research limitations/implications The model assumes linear elasticity and does not consider thermal effects or material nonlinearity. Future research may include viscoelastic behavior and temperature-dependent properties for enhanced accuracy. Practical implications The findings provide a reliable analytical tool for engineers to predict and enhance the stability performance of tapered beams in civil and mechanical structures, particularly under dynamic loads. Social implications Improving the structural resilience of dynamically loaded beams enhances public safety in infrastructures such as bridges, towers, and pipelines, reducing risks during seismic or variable load events. Originality/value This research offers a novel application of the Rayleigh-Ritz and Bolotin methods for dynamic buckling analysis of non-prismatic beams on elastic foundations. The approach enables high computational efficiency and accuracy validated against existing studies.