Frequency identification of non-beam bridges using vehicle scanning methods: Analytical formulation and experimental validation

Abstract

This article presents a novel analytical formulation that demonstrates how the natural vibration frequencies of any bridge - regardless of its structural type, geometry, or boundary conditions - can be identified from the vibrations recorded by an instrumented vehicle crossing the bridge. This formulation broadens the scope of vehicle scanning methods for bridge frequency identification by removing the traditional assumption of sinusoidal mode shapes, which previously limited their application to simply supported beam bridges. The methodology begins by expanding bridge vibrations using a Fourier series, demonstrating that only the natural frequencies of the bridge contribute nonzero terms to this expansion. This is universally applicable, independent of bridge typology and geometry. Using Duhamel’s integral, the response of a vehicle traversing the bridge was computed to analytically prove that the bridge’s natural frequencies appear in the vehicle’s vibration spectrum. To validate the formulation, we present two applications. First, a numerical study models an 80 m steel arch bridge, confirming its non-sinusoidal mode shapes through eigenvalue analysis. A virtual vehicle crossing simulation reveals that the bridge’s natural frequencies are clearly identifiable in the Fourier amplitude spectrum (FAS) of the vehicle vibrations. Second, a field test is conducted on a 602 m cable-stayed bridge using an instrumented vehicle equipped with low-cost roof-mounted accelerometers. The first three modal frequencies of the bridge are successfully extracted from the vehicle’s recorded vibrations, demonstrating the practical feasibility of the developed formulation in real-world conditions.

Topics & Concepts