动静阻尼影响下锚杆瞬态动力响应的解析解及工作状态预测

为了分析动静阻尼条件下锚杆的瞬态动力响应特征以及荷载与锚杆振动基频之间的相互关系，在考虑锚固介质对锚杆产生的动态与静态阻尼力的影响下，基于波动理论建立了锚杆受瞬态激振时引起弹性振动的波动方程。在一端固定一端自由的边界条件下，求解锚杆位移场的解析解，得到基频与荷载之间呈二次幂函数关系。为了验证理论分析的结果，采用室内模型锚杆的拉拔试验和无损检测试验，对不同加载等级下的动测信号进行频谱分析得出对应的基频，采用最小二乘法拟合得到荷载与基频之间的函数关系也呈二次幂函数关系，且施加的荷载小于锚杆体与锚固介质间的握固力时，荷载与基频呈正相关关系，荷载大于握固力时，二者呈负相关关系，这与理论分析结果基本吻合。

Analytical solution of transient dynamic response and working condition prediction of bolt considering dynamic and static damping

In order to analyze the characteristics of transient dynamic response and the relationship between loads and vibration fundamental frequencies of the bolt in the role of damping，in considering the impact of anchoring medium of the bolt on dynamic and static damping and based on wave theory，the wave equation，which is about the elastic vibration of the bolt when suffered by transient excitation，was established.Analytical solution of displacement field of the bolt was solved under the boundary condition that it is fixed at the one end of the bolt and it is free at the other end of the bolt.The theoretical result shows there is a second order power function relationship between the fundamental frequency and load.In order to verify the theoretical result，the pullout test and nondestructive test of the indoor model bolts were used，through the spectrum analysis of the dynamic testing signals，the fundamental frequency was obtained under the corresponding load.Fitting function relationship between load and fundamental frequency by using the least squares also presents a second order power function relationship，the load and fundamental frequency are positively correlated when the load is less than the grip between the medium and bolt-rod，but it is the negative correlation between both when the load is more than the grip，and the results are consistent with the theoretical analysis.