ZHANG X M, SHI Y L, TIAN X G,,et al.Theoretical calculation and numerical simulation of the characteristics of longitudinal guided wave in resin bolts[J].Journal of Henan Polytechnic University(Natural Science) ,2026,45(1):118-127.

doi:10.16186/j.cnki.1673-9787.2023040048

Received:2023/04/23

Revised:2023/08/06

Published:2025-12-03

Theoretical calculation and numerical simulation of the characteristics of longitudinal guided wave in resin bolts

Zhang Xiaoming1, Shi Yulong1, Tian Xiaoguang2, Li Zhi1

1.School of Mechanical and Power Engineering， Henan Polytechnic University， Jiaozuo  454000， Henan， China；2.No. 11 Mine of Pingmei Coal Group ， China Pingmei Shenma Holding Group Co.， Ltd.， Pingdingshan  467000， Henan， China

Abstract: Objectives To illustrate the characteristics of longitudinal guided wave in resin bolts， the eigenfunction expansion method was used to solve the longitudinal guided wave dispersion equations of a resin bolt. Methods The resin anchor bolt was considered as a typical double-layer cylindrical viscoelastic structure. Based on the Hysteretic viscoelastic model， considering continuity boundary conditions， the acoustic field displacements were represented in the Legendre polynomial series form. Then the problem of solving the complex wave control partial differential equation system was transformed into the problem of eigenvalue calculation through matrix transformation. The eigenvalue was the wave number， and the eigenvector was the displacement field distribution， the longitudinal guided wave dispersion relationship was established， and the analytical solution of the transcendental dispersion equation was obtained. Then the group velocity dispersion curve and attenuation curve could be plotted. The correctness of the presented method was verified by comparing the obtained group velocity and attenuation results of a free bolt with those of existing literature. Based on the COMSOL software， the longitudinal guided waves in various resin bolts were simulated to illustrate the influences of resin layer thickness and bond length on the guided wave characteristics. Results The results showed that： （1） The thickness of the resin layer had a significant effect on the longitudinal guided waves. With the increase of layer thickness， the wave packet dispersion and waveform distortion of the recovered signal increased. The group velocity and amplitude ratio of guided waves decrease with the increase of layer thickness， but the attenuation increased. （2） With the increase of bond length， the group velocity of guided waves in the resin bolt decreased， the amplitude ratio decreased， and the guided wave attenuation increased. Conclusions The group velocity of guided wave was approximately linear with the bond length， and quantitative judgment of the length of the resin bolt bond section can be made through changes in guided wave group velocity.

Key words:resin bolt;longitudinal guided wave;eigenfunction expansion method;group velocity;attenuation