# Calculation of the modal parameters of a suspension bridge

Version 3.3 (161 KB) by
The eigenfrequencies and modes shapes of a suspension bridge are calculated using a continuum model
Updated 8 May 2020

# eigenBridge

## Summary

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

Cheynet, E. Calculation of the Modal Parameters of a Suspension Bridge. Zenodo, 2020, doi:10.5281/ZENODO.3817982.

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##### MATLAB Release Compatibility
Created with R2019b
Compatible with any release
##### Platform Compatibility
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Version Published Release Notes
3.3

See release notes for this release on GitHub: https://github.com/ECheynet/eigenBridge/releases/tag/v3.3

3.2.0.0

See release notes for this release on GitHub: https://github.com/ECheynet/eigenBridge/releases/tag/v3.2

3.1

Added the project website

3.0.0.0

Title
The lateral mode shapes of the deck include now properly the influence of the cable motion
Title
typo

2.0.0.0

-Example file provided + many simplifications

1.2.0.0

- possibility to use a different young modulus for main cables

1.1.0.0

- separation into more modules for sake of clarity (new matlab file "ExampleBridge.m" included)
- For those interested only in one degree of freedom, the inputs have been sorted on a more visible way.

1.0.0.0

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- typo and description
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To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.