集中静荷载初始效应对固支梁固有频率的影响

Influence of the initial effect of concentrated static load on natural frequencies of fixed beams

研究了集中静荷载初始效应对于固支梁固有频率的影响,利用能量守恒方程和变分原理,得到了存在初始挠度时梁的振动控制方程。在此基础上,分析得到了存在初始挠度时梁固有频率的解析解,以及存在初始集中静荷载时固支梁的固有频率和固有振型的变化规律,分析比较了高跨比、梁上集中静荷载大小等因素对于固有频率的影响,并开展了相应的室内试验。结果表明:对于同一固支梁,固有频率随梁上静荷载的增大呈线性增大趋势;对于两端固支的3mm梁,初始挠度对固有频率的影响可达到17.3%;随着梁高跨比的减小,初始挠度对固有频率的影响逐渐增大。因此,实际的桥梁结构设计中,应充分考虑初始挠度对固有频率的影响。

Influence of concentrated static load on natural frequencies of fixed beams is investigated in this paper. The governing equations of beam with initial deflection are obtained by energy conservation equation and variational principle. On this basis, the analytical solution of natural frequency of the beam with initial deflection is calculated, and the variation law of natural frequency and natural mode of fixed beams with initial concentrated static load is revealed. The influence of high span ratio and concentrated static load on the natural frequency is analyzed and compared, and the corresponding model test is carried out. For the same fixed beam, the natural frequency increases linearly with the increase of the static load on the beam. The influence of initial deflection on natural frequency of 3mm fixed beam can be up to 17.3%. With the decrease of high span ratio, the influence of initial deflection on natural frequency increases. Therefore, the influence of initial deflection on natural frequency should be fully considered in actual bridge structure design.