**Natural mode shapes and frequencies**
**Natural mode shapes and frequencies of bridge at deadload**
Natural mode shapes and frequencies (nmf) of bridge are fundamental to the solution of its dynamic responses due to seismic, wind and traffic loads. The nmf is depended on the particularities and characteristics of the bridge such as the bending and torsional stiffness of the stiffening girder, the pylon, the hanger's distance between the two cables (in transverse and longitudinal direction) and the support conditions. By changing nmf, one will get a significant change in results of the dynamic analysis. However, the eigenvalues (frequencies) and the eigenvectors (mode shapes) of a bridge are obtained already after Loadcase1 Initial Forces and Loadcase2 Deadload has been convergent successfully. I.e. the nmf are depended on the initial tensions of the cables, the structural weight of the bridge's elements, but not on the vehicle weighs. Thus, optimization of the nmf should be done before the analysis of the live loads on bridge because the eigenvalue analysis can lead to the necessary changes of structural dimensions. The case a static analysis lead to the changes of structural dimensions, a new eigenvalue analysis should be performed again. In LUSAS 15.0-* we can solve a selected analysis so we can perform the analysis we need. Vibrations of a cable-stayed bridge can be distinguished on the global and local modes. The global modes are where the pylons, the girder and all cables are vibrated in the same frequency, typically identified by the motions of the pylons and the deck. In these modes the non-vibration cables just follow the motions of the pylons and the deck. The local modes are referred to vibrations of some single cables, with significant bigger amplitudes than the pylons and the deck. However, there are also some modes where the dominant vibrations of the cables occur in the same frequency of visible vibrations of the deck and the pylons, as shown in mode 9 to 11 below. It should be noted that mode shapes of the cables are most realistic when they are fine division in many elements (which need more time to reach convergence). The model below has the longest and the shortest cables of 160.2m and 37.9m, respectively. They are all modeled in 2m element, i.e. there are 19 elements (of thick nonlinear beam) in the shortest cable. Finally, solution for the mode shapes below allow the cables to be shorter and longer, as shown in mode 9 below for the short cables at the pylon. The following abbreviations are used with respect to the vibrations of the deck Symmetric Lateral (SL) Asymmetric Lateral (AL)
Symmetric Vertical (SV) Asymmetric Vertical (AV)
Symmetric Torsional (ST) Asymmetric Torsional (AT)
Updated 31-01-2015 |