A new analytical solution for fundamental frequencies of cable suspension bridge with unsymmetric side spans.

One of the main approaches in monitoring the integrity of cable suspension bridges is the continuous measurement of the natural frequencies of a bridge. Cracking or damaging in a bridge will lead to the softening of the structures, and thus results in the degradation of natural frequency of the bridge. However, accurate identification of the modes of each natural frequency that they are associated with is important. It is because when the degradation of a particular natural frequency is observed, mode identification of that decreasing frequency normally points us to the location of damages. With the advances of computer and finite element method, some argue that the problem can be easily solved.  In reality, it has been observed that even the fundamental frequency from field measurement differs quite significantly with that of FEM result. The actual detailing of a bridge, variations of material properties, joint fabrications, and workmanship all affect the actually vibrations frequency. FEM idealization is extremely difficult. In reality, simple analytic formulas were given for idealized cases. For example, there is no analytical formula for the vibration frequency of cable suspension bridge with unsymmetric side spans. But due to constraints from geology or geography, side spans may not be designed in a symmetric manner. Huangpu Bridge with main span of 1108m over the Pearl River at Guangzhou is a good example. The width of the bridge deck is 41.69m, which is the widest suspension bridge deck in the world. In this paper, we derive a new analytical solution for natural frequency of cable suspension bridge with unsymmetric side spans. The method of solutions is modified from Rocard (1957). References: Rocard, Y. (1957) Dynamic instability : automobiles, aircraft, suspension bridges, London, C. Lockwood