Calculation of the modal parameters of a suspension bridge
Updated 8 May 2020
The calculation of the eigenfrequencies and mode shapes of a suspension bridge using the present Matlab code is based on the theory of continuous beam and the theory of shallow cables. The mode shapes are obtained using Galerkin's method where a series expansion is used. The method was first applied by Sigbjörnsson & Hjorth-Hansen . E. Strømmen  expanded their works to the vertical and torsional motion.
The bridge is represented as a horizontal streamlined beam, where the z-axis is the vertical axis, the y-axis is the along-beam axis and the x-axis is the cross-beam axis. The three motions of interests (lateral, vertical, and torsional) and both symmetric and asymmetric modes are computed.
- eigenBridge is a function that computes the mode shapes and eigenfrequencies of the suspension bridge
- Documentation.mlx: is an example of the application of this function
 Sigbjönsson, R., Hjorth-Hansen, E.: Along wind response of suspension bridges with special reference to stiffening by horizontal cables. Engineering Structures 3, 27-37 (1981)  Structural Dynamics, Einar N Strømmen, Springer International Publishing, 2013. ISBN: 3319018019, 9783319018010 Characteristics of the single-span suspension bridge
Cheynet, E. Calculation of the Modal Parameters of a Suspension Bridge. Zenodo, 2020, doi:10.5281/ZENODO.3817982.
MATLAB Release Compatibility
Platform CompatibilityWindows macOS Linux
- MATLAB > Mathematics > Numerical Integration and Differential Equations >
- Physical Modeling > Simscape Multibody > Multibody Modeling >
Inspired: Automated vehicle identification using bridge vibrations, Static analysis - Suspension bridge - A benchmark solution, Buffeting response of a suspension bridge (time domain), Mode shapes extraction by time domain decomposition (TDD), Flutter velocity of a suspension bridge, Dynamic response of a line-like structure to a random load, Buffeting response of a suspension bridge (frequency domain), Linear vertical vibrations of suspension bridges
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See release notes for this release on GitHub: https://github.com/ECheynet/eigenBridge/releases/tag/v3.3
Added the project website
-Example file provided + many simplifications
- possibility to use a different young modulus for main cables
- separation into more modules for sake of clarity (new matlab file "ExampleBridge.m" included)