Dynamic Modeling and Analysis of Multi-Span Timoshenko Beams Under Moving Loads

Dynamic response analysis of multi-span beams is one of the important topics in the field of highway and railway engineering, which provides valuable guidance for the design, operation and maintenance of multi-span bridges. It is worth considering how to calculate the dynamic characteristics of multi-span beams quickly and conveniently. In this study, an effective analytical method is developed for the dynamic modeling and investigations of multi-span Timoshenko beams under moving loads by employing the assumed mode method (AMM). Based on Hamilton’s principle, the equation of motion of the Timoshenko multi-span beam subjected to moving loads is formulated and the natural frequencies are calculated. A comprehensive investigation is conducted on the dynamic responses of the multi-span Timoshenko beam considering different factors, including the length-to-thickness ratio, disorder degree, arrangement order, number of spans and related parameters of moving loads. In addition, the influence of the interval and velocity of the moving load series on the dynamic responses, including displacement, velocity and acceleration of the multi-span beam, are analyzed in detail. The theoretical calculation results of multi-span Timoshenko beams under moving loads are compared with numerical results obtained from ANSYS software, and the results are in good agreement. This demonstrates that the developed method, which utilizes the AMM to analyze the dynamic characteristics of multi-span beams subjected to moving loads, significantly simplifies the calculations and is well-suited for practical engineering applications.