Analytical and numerical study on free vertical vibration of shear-flexible suspension bridges

This study develops an analytical and numerical method for free vertical vibration of suspension bridges including shear deformation and rotary inertia. Under the assumption that the vertical displacement of the main cable is identical to that of the stiffening girder, the differential equation of motion containing three new terms are derived based on Timoshenko's beam-column theory. The general analytical method for determining natural frequencies and mode shapes of hinged- and continuous-suspension bridges are presented. Special consideration is given is evaluating the natural frequency of simply supported three-span suspension bridges. For finite element analysis, the suspension bridge element is developed by using Hermitian polynomials considering shear effects. The full truss model, in which both cable and truss girder is modelled by a truss element, is used in order to investigate the accuracy of the presented suspension bridge theory. Numerical examples are provided to illustrate the applicability and effectiveness of the present analytical and numerical method.