Geodesic
The approximation function of bridge deck vibration derived from the measured eigenmodes
International Journal of Applied Mathematics and Computer Science, Tome 27 (2017) no. 4, pp. 799-814.

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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.
Keywords: eigenmode approximation, eigenmode derivatives, regression spline, spectral analysis, distributed parameter system
Mots-clés : krzywa regresji, analiza spektralna, układ o parametrach rozłożonych 
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Sokol, M.; Komorníková, M.; Bacigál, T.; Rodríguez, M. X. The approximation function of bridge deck vibration derived from the measured eigenmodes. International Journal of Applied Mathematics and Computer Science, Tome 27 (2017) no. 4, pp. 799-814. http://geodesic.mathdoc.fr/item/IJAMCS_2017_27_4_a10/

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