Vibration Mode Analysis of a 100m Simply-supported Steel Beam Bridge via POD of FEM

Abstract

Bridge vibrations pose significant challenges to structural safety and longevity. This study employs the Finite Element Method (FEM) with Euler-Bernoulli beam elements and Proper Orthogonal Decomposition (POD) to analyze the dynamic response of a one-dimensional beam bridge model under sinusoidal external loading. The governing partial differential equation (PDE) describes the behavior of the lines with terms for inertial forces, damping, and flexural rigidity, discretized into a system of algebraic equations using finite elements of a 1D beam. This numerical approach simulates the bridge’s linear displacement field over time and space, providing detailed understanding of its vibrational behavior through POD mode extraction. This study highlights the importance of integrating advanced computational tools, such as FEM and POD, into structural engineering practices. Furthermore, this research promotes the safe and sustainable development of infrastructure, particularly in the Pacific region, where rising sea levels and extreme weather events pose significant challenges.