Extension of a semi-analytical approach to determine natural frequencies and mode shapes of a multi-span orthotropic bridge deck

Abstract

Abstract. This paper extends a single equation, semi-analytical approach for three-span bridges to multispan ones for the rapid and precise determination of natural frequencies and natural mode shapes of an orthotropic, multi-span plate. This method can be used to study the dynamic interaction between bridges and vehicles. It is based on the modal superposition method taking into account intermodal coupling to determine natural frequencies and mode shapes of a bridge deck. In this paper, a four-and a five-span orthotropic roadway bridge decks are compared in the first 10 modes with a finite element method analysis using ANSYS software. This simplified implementation matches numerical modeling within 2% in all cases. The paper verifies that applicability of single formula approach as a simpler alternative to finite element modeling.

Free vibration analysis of multi-span orthotropic bridge deck with rubber bearings

“…To incorporate the intermodal coupling, the solution adopted herein for eq. 4is that which was previously proposed [12,13], where Wij(x,y) is expressed as the product of two admissible functions:  is a frequency parameter of the mul-ti-span beam. Zhu and Law [5] presented the formulation of the eigenfunctions and mode shapes of a multi-span, continuous beam with rotational and linear springs.…”

“…Notably their decomposition of mode shapes did not incorporate the intermodal coupling caused by the mixed derivatives that appear in the formulation of free edge plate conditions [11]. In affiliated work, a semi-analytical approach to determine natural frequencies and mode shapes of an orthotropic, multispan plate with rigid line supports was introduced by Rezaiguia and Laefer [12] and Rezaiguia et al [13] based on modal superposition and the inclusion of intermodal coupling. When compared to FEM models, the mode shapes matched, and the frequencies were within 2%, despite the approach's comparative simplicity, thereby making it a good candidate to study the dynamic interaction between bridge decks and vehicles.…”

“…In commercial bridge design, rubber supports are modelled as a two-joint link aligned vertically, in such a way that one end is connected to the bridge deck and the other end is fixed as per Kunde and Jangid [14]. The following research extends modal superposition with the intermodal coupling approach [12,13] through the inclusion of elastic, line supports. Specifically, the vertical displacement of the plate is obtained by modal superposition.…”

Dynamic amplification of a multi-span, continuous orthotropic bridge deck under vehicular movement

“…where q ij (t) are the modal coordinates,  ij (x,y) are the mode shapes of a thin, orthotropic multi-span plate (taking into account intermodal coupling, which is associated with the natural frequencies  ij , as detailed in references [28] and [29]). …”