Linear vertical vibrations of a suspension bridge

Summary

The vertical eigenfrequencies and mode shapes of a single-span suspension bridge are computed using the method by Luco et Turmo [1]. For the sake of completeness, the computed modal parameters are compared with those obtained using the method by Sigbjørnsson & Hjorth-Hansen [2] and Strømmen [3].

Content

The submission contains:

• 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 in a numerical way.
• eigBridge_Verification.m: its only purpose is to verify the numerical implementation of eigenBridge2.m
• Verifications.mlx : It is a verification of the works of [4], where I try to obtain exactly what [4] show in their paper.
• Application.mlx: I compare eigenBridge.m with eigenBridge2.m

Any comment or idea of improvement is warmly welcome.

References

[1] 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