Modeling and modal analysis of suspension bridge based on continual formula method

摘要

A continnum model is developed for the dynamic analysis of a suspension bridge with inclined main cables and hangers, based on incremental Lagrangian formulation and kinematics theories. The static equilibrium equations are derived from a shape-finding method followed by the equations of motion. Comparison of modal analysis results of the proposed model and the finite element method demonstrates the accuracy of the proposed modelling technique. Modal analysis is further conducted with variations of the following system parameters, i.e. inclination angle of main cable, the ratio of flexural stiffness of deck in the vertical and lateral directions, the ratio of vertical flexural stiffness of deck and tensile stiffness of cable, and torsional moment of inertia of cross-section of deck. Results show that the difference of eigenfrequencies within the eigenfrequency cluster is smaller for a suspension bridge with vertical cables than that with inclined cables. Phenomena of crossover and veering of eigenfrequency loci of the bridge system are observed. The mechanism of such phenomena is further studied with the help of a sectional bridge model. The effect of variation of stiffness matrix of bridge system on the eigenfunction is studied. The condition for crossover and veering of the eigenfrequency loci of this bridge model is identified. It is noted that veering can affect the modal property of the system by coupling two involved modes. This effect should be carefully examined during the design of the suspension bridge.