Semi-analytical determination of natural frequencies and mode shapes of multi-span bridge decks

The determination of the natural frequencies and mode shapes of structures requires an analytical, semi-analytical or numerical method. This paper presents a new semi-analytical approach to determine natural frequencies and mode shapes of a multi-span, continuous, orthotropic bridge deck. The suggested approach is based on the modal method, which differs from other approaches in its decomposition of the admissible functions defining the mode shapes. Implementation of this technique is simple and enables avoidance of cumbersome mathematical calculations. In this paper, application of the semi-analytic approach to a three-span, orthotropic roadway bridge deck is compared in the first 16 modes of previously published fully analytical results and to a finite element method analysis. The simplified implementation matches within 2 % in all cases, with the additional benefit of including intermodal coupling. The approach can be extended to similar bridges with more than three spans.