Comparison of several methods for calculating vibration mode shape derivatives

This article deals with a method of how to acquire approximate displacement vibration functions. Input values are discrete, experimentally obtained mode shapes. A new improved approximation method based on the modal vibrations of the deck is derived using the least-squares method. An alternative approach to be employed in this paper is to approximate the displacement vibration function by a sum of sine functions whose periodicity is determined by spectral analysis adapted for non-uniformly sampled data and where the parameters of scale and phase are estimated as usual by the least-squares method. Moreover, this periodic component is supplemented by a cubic regression spline (fitted on its residuals) that captures individual displacements between piers. The statistical evaluation of the stiffness parameter is performed using more vertical modes obtained from experimental results. The previous method (Sokol and Flesch, 2005), which was derived for near the pier areas, has been enhanced to the whole length of the bridge. The experimental data describing the mode shapes are not appropriate for direct use. Especially the higher derivatives calculated from these data are very sensitive to data precision.

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“…Finally, taking into account equation (15) and substituting equations (17) and (20) in it, the rank of the sensitivity matrix [S] is given by…”

Section: Limits Of Dynamic Model Updatingmentioning

confidence: 99%

“…Variations and modi"cations are to be found in references [12}14]. All of these have been compared in reference [15], where it is concluded that the Nelson method o!ers the best computational performance.…”

Section: Introductionmentioning

confidence: 99%

On Theoretical Limits of Dynamic Model Updating Using a Sensitivity-Based Approach

Gola

Somà

Botto

2001

Journal of Sound and Vibration

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Comparison of several methods for calculating vibration mode shape derivatives

Cited by 92 publications

References 7 publications

Detection of Spring Support Locations in Elastic Structures Using a Gradient-Based Finite Element Model Updating Technique

Detection of Spring Support Locations in Elastic Structures Using a Gradient-Based Finite Element Model Updating Technique

The approximation function of bridge deck vibration derived from the measured eigenmodes

On Theoretical Limits of Dynamic Model Updating Using a Sensitivity-Based Approach

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