Vertical Vibration in Timoshenko Beam Suspension Bridges

Abstract

A method of analysis is presented for free vertical vibration of suspension bridges. The method takes into account the effects of shear deformation and rotary inertia, and uses a linearized theory which maintains small amplitudes of vibration. The formulation of the problem is based on the Timoshenko beam theory, and the differential equations of motion and the associated boundary conditions are derived by applying Hamilton's principle. The analysis is conducted by using general solutions for the fourth order differential equation of motion. The objective of the study is to determine a sufficient number of natural frequencies and mode shapes, and to enable an accurate vibration analysis for higher modes. A detailed numerical example, which includes the various boundary conditions of the stiffening girders and the elasticity of the towers, is shown to illustrate the applicability of the analysis and to investigate the dynamic characteristics of vertical vibrating suspension bridges.