Improved Continuum Model for Free Vibration Analysis of Suspension Bridges

Abstract

An improved continuum model of three-span suspension bridges has been developed to study the effects of hanger extensibility on free vertical vibrations. This model can be applied to both hinged and continuous girders. To obtain the equations of motion, coupled differential equations describing the vertical deflections of the main cable and the girder are derived with dimensionless parameters. Following the Galerkin method, with shape functions for the main cable and for hinged and continuous girders, equations of motion are obtained in matrix form. A compatibility equation is used to eliminate the additional horizontal force of the main cable in the equations. Natural frequencies of hinged and continuous suspension bridges are evaluated as a function of six dimensionless parameters: the relative elastic bending stiffness of the girder, the relative elastic axial stiffness of the main cable, the relative elastic axial stiffness of the hangers, the relative mass of the girder, the relative length of the side span, and the ratio of the main span sag to the maximum hanger length. Parametric studies are conducted in which each of these parameters is varied individually to observe its effect on the natural frequencies and to identify differences between a conventional model with inextensible hangers and the improved model with extensible hangers. It is found that hanger extensibility affects the natural frequencies and mode shapes of higher modes for suspension bridges with a large relative girder stiffness. This effect is slightly more pronounced for antisymmetric modes and continuous bridges. In addition, even for a bridge with a large relative girder stiffness, the hanger extensibility rarely affects the natural frequencies of higher modes if the bridge either has a large relative mass of the girder or a large relative length of the side span.