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Paper details
Number 4 - December 2017
Volume 27 - 2017
The approximation function of bridge deck vibration derived from the measured eigenmodes
Milan Sokol, Magdaléna Komorníková, Tomáš Bacigál, Miguel X. Rodríguez
Abstract
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