Suspension Bridge Vibration: Continuum Formulation

The methodology of the free vibration analysis of suspension bridges with horizontal decks is refined and extended, utilizing a continuum approach to include both the coupled vertical-torsional vibration and the effect of cross-sectional distortion. Variational principles are used to obtain the coupled equations of motion in their most general, and nonlinear form. The general equations are linearized, eliminating the coupling effect, and solved for a specific bridge; the resulting natural frequencies and modes of vertical and torsional vibrations are compared with those calculated using the finite element approach and with those estimated from low-amplitude full-scale ambient vibration tests which were conducted on the bridge. In addition, the general, nonlinear equations of motion governing the lateral vibration of suspension bridges are presented and the linearized forms are obtained; a numerical example and a comparison among the analytical, numerical and full-scale test results are also presented.