移动荷载列作用下简支梁振动响应参数研究

推导了移动荷载列作用下简支梁位移响应的精确解,在此基础上引入3个无量纲参数,研究了荷载移动速度、荷载频率及结构阻尼对桥梁响应的影响,分析了简支梁在一定荷载速度下的共振和消振现象发生机理。结果表明:桥梁跨中的最大位移响应并非随着荷载速度的增大而单调地增大,而是表现出一种类似正弦但波幅逐渐变大的方式;当移动荷载列以消振速度通过桥梁时,引起的桥梁余振响应趋近于零;简支梁的共振速度与移动荷载列的间距有直接关系,当共振速度同时又是消振速度时,共振现象被抑制;当简谐荷载移动速度较低时,梁体位移在荷载频率等于梁体第一阶自振频率时达到最大响应,随着荷载移动速度的增大,梁体位移达最大响应不再发生于荷载频率等于梁体第一阶自振频率的情况。

Dynamic Response Parameter Analyses of Simply-supported Beam under Moving Load Series

The exact displacement solution of the dynamic equation of a simply-supported beam under moving load series is derived. Three dimensionless parameters are introduced to study the influence of load speed, load frequency and structural damping on the dynamic responses of the beam, and analyze the mechanism of resonance and vibration cancelation mechanism of simply-supported beam under moving load. The results show that the maximum displacement at the mid-span increases in a sinusoidal form with gradually increasing amplitude, instead of in a monotonous way. The residual displacement and velocity of the beam close to zero when the load series pass through at a vibration elimination speed. The resonance speed obtained by the calculation of the load interval, the resonance will be suppressed, when the resonance speed is also the vibration elimination speed. When the speed of harmonic load is low, the displacement of the beam will achieve maximum under condition of the load frequency equals to the first-order frequency of the beam; while the displacement of the beam will achieve maximum under condition of the load frequency not equals to the first-order frequency of the beam, if the speed of harmonic load is high.