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 vibra- tion 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 fre- quency 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.