The approximation function of bridge deck vibration derived from the measured eigenmodes. (English) Zbl 1396.70025
Summary: 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 developed by M. Sokol and R. Flesch [Assessment of soil stiffness properties by dynamic tests on bridges, ASCE Journal of Bridge Engineering 10, No. 1, 77–86 (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.
MSC:
| 70L05 | Random vibrations in mechanics of particles and systems |
| 93B60 | Eigenvalue problems |
| 93E25 | Computational methods in stochastic control (MSC2010) |
Keywords:
eigenmode approximation; eigenmode derivatives; regression spline; spectral analysis; distributed parameter systemReferences:
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