Calculation method of natural characteristics of beam element considering initial state

Abstract

Natural frequencies and modal shape play an important role in the analysis of the dynamic characteristics of long-span bridges including wind resistance and seismic. The initial static load, which caused by overloading, etc., has a certain impact on the natural characteristics. Therefore, the initial effect of static load on the inherent characteristics of the beam is studied. The vibration control equation of beam with initial state is obtained by using the energy conservation equation and Hamilton principle. Under different boundary conditions, the analytical solution of the natural frequency considering the initial state, and the influence law of the initial static load and the height-span ratio on the natural characteristics are obtained. The results show that the increase in the deflection of the beam caused by the static load will increase the stiffness of the beam, and further lead to the change of the natural characteristics of the beam. Therefore, in the analysis of the natural characteristics of the bridge, the influence of the initial state caused by static load should be fully considered.