Influence of Variable Prestress on the Dynamic Performance of an Elastically Supported Euler–Bernoulli Beam Under Moving Distributed Loads

Abstract

The dynamic behavior of beam-type structures subjected to moving loads is of considerable importance in civil, mechanical, and transportation engineering, particularly in the design of bridges, railway tracks, conveyor systems, and other structural components where serviceability and structural safety are governed by vibration performance. Prestressing has been widely employed to improve structural stiffness and reduce deflection; however, the influence of variable prestress on the dynamic response of elastically supported beams under moving distributed loads has received comparatively less attention. This study investigates the influence of spatially varying prestress on the dynamic performance of an elastically supported Euler–Bernoulli beam subjected to moving distributed loads. A mathematical model is formulated by incorporating the combined effects of variable prestress, elastic foundation stiffness, and moving load characteristics into the governing beam equation. The resulting partial differential equation is solved analytically to determine the transient dynamic response of the beam. Parametric investigations are conducted to examine the influence of prestress variation, foundation stiffness, load velocity, and load distribution length on beam deflection and vibration characteristics. The results show that the increasing tensile prestress substantially reduces the maximum dynamic deflection and vibration amplitude, whereas compressive prestress increases the dynamic response and may compromise structural stability. Furthermore, greater foundation stiffness effectively suppresses beam vibrations and improves structural performance, particularly under high-speed moving loads.The study demonstrates that the combined optimization of prestress distribution and elastic foundation properties provides an effective strategy for controlling beam vibrations and enhancing the dynamic performance of engineering structures subjected to moving distributed loads.