This study investigates the dynamic behaviour of an elastically supported uniform Rayleigh beam subjected to the passage of moving distributed masses with varying velocities, where the loading conditions vary arbitrarily with time. The motion of this problem is described by a fourth-order partial differential equation, which governs its behaviour. The beam’s non-stationary response under such dynamic loading scenarios is analysed using the weighted residual method, which converts the governing equation into a sequence of linked second-order differential equations to facilitate the analysis. A rewritten version of Struble’s asymptotic method further simplifies the transformed governing equation. This modification aids reduction in the complexity of the equation. The closed-form response is contrasted for the acceleration and deceleration motion. The study thoroughly examines how different velocities and frequencies of the moving force affect the dynamic behaviour of the beam. Key aspects explored include the influence of axial force, foundation modulus, and shear modulus in the support structure, the impact of varying mass distributions, and the time-dependent nature of the applied loads. The results help further understand the structural dynamics in complex environments and offer insights into optimising the design and performance of similar systems under non-stationary dynamic loads.

Soil stabilization is a ground improvement technique aimed at enhancing the strength and bearing capacity of soil, particularly in road construction projects. The combination of multiple stabilization materials allows for achieving better improvements in soil bearing capacity. The use of industrial waste materials offers an eco-friendly solution while repurposing materials that are typically discarded. This study focuses on the engineering application of adding limestone as a natural pozzolanic material. The research involves laboratory testing to measure the unconfined compressive strength (UCS) of stabilized clay soil samples. The addition of stabilization materials is based on weight ratios, where the ratio of nickel slag to aluminum hydroxide is 1,5, and limestone is added in varying proportions of 2%, 4%, and 6%. The curing of the test specimens is carried out over periods of 3, 7, 14, and 28 days to examine the influence of curing time on the improvement of soil UCS values. The results indicate that the addition of nickel slag and aluminum hydroxide significantly enhances the soil’s UCS. Furthermore, variations in limestone content show that increasing its concentration up to 6% yields optimal results in improving soil strength. This study concludes that the combination of waste materials and limestone can effectively enhance the mechanical characteristics of soil, providing a sustainable and environmentally friendly solution for soil stabilization in various infrastructure projects.