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Linear vertical vibrations of suspension bridges

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The eigen-frequencies and mode-shapes for the vertical DOF of a suspension bridge are computed



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I have previously submitted a Matlab function on fileExchange (File ID: #51815) to compute the eigen frequencies and mode shapes of a suspension bridge following [5,6]. However this is not the traditional method. I have therefore attached a more classical formulation, entirely inspired from [4] that I believe is particularly pedagogical. I only focus on the vertical DOF here. I am using the example of Lysefjord Bridge, of which information is available from [1,2,3].

The submission contains 3 Matlab functions:
- eigenBridge.m (it is identical to File ID: #51815) and is inspired from [5,6]
- eigenridge2.m based on works of [4]. I am simply writing the equations and their solutions on a numerical way.
- eigBridge_Verification.m: its only purpose is to verify the numerical implementation of eigenBridge2.m

In additions, 2 examples files are included:
- Verifications.m : It is a verification of the works of [4], where I try to obtain exactly what [4] show in their paper.
- Application.m: I compare eigenBridge.m with eigenBridge2.m

All the credits go to the authors [1-6] for the original works. This is the first version of the submissions. Several changes might be expected. Any comment or idea of improvement is warmly welcome. If you find a bug, please notify it!


[1] Opsahl Steigen, R. (2011). Modeling and analyzing a suspension bridge in light of deterioration of the main cable wires.

[2] Tveiten, J. (2012). Dynamic analysis of a suspension bridge.

[3] Gran, B. (2012). Konstruksjonsanalyse av en hengebro.

[4] Luco, J. E., & Turmo, J. (2010). Linear vertical vibrations of suspension bridges: A review of continuum models and some new results. Soil Dynamics and Earthquake Engineering, 30(9), 769-781.

[5] Sigbjørnsson, R., Hjorth-Hansen, E.: Along wind response of suspension bridges with special reference to stiffening by horizontal cables. Engineering Structures 3, 27–37 (1981)

[6] Structural Dynamics, Einar N Strømmen, Springer International Publishing, 2013. ISBN: 3319018019, 783319018010

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