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## Calculation of the modal parameters of a suspension bridge

version 3.3 (161 KB) by E. Cheynet

### E. Cheynet (view profile)

The eigen-frequencies and modes shapes of a suspension bridge are calculated on a simple way

Updated 08 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 [1]. E. Strømmen [2] 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.

Content:
- 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

References:

[1] 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)
[2] Structural Dynamics, Einar N Strømmen, Springer International Publishing, 2013. ISBN: 3319018019, 9783319018010 Characteristics of the single-span suspension bridge

### Cite As

E. Cheynet (2020). Calculation of the modal parameters of a suspension bridge (https://www.github.com/ECheynet/eigenBridge), GitHub. Retrieved .

E. Cheynet. ECheynet/EigenBridge v3.3. Zenodo, 2020, doi:10.5281/ZENODO.3817982.

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