Axial stress measurement of long threaded fasteners based on dual-frequency L(0,1) guided waves

A novel axial stress measurement method for long threaded fasteners leveraging dual-frequency guided-wave detection was proposed. By integrating acoustoelastic theory with numerical simulations, the stress-dependent Time-of-Flight (TOF) relationship was formulated, and mathematical models for both single-frequency and dual-frequency detection strategies were established. The propagation behaviour of guided waves under varying excitation frequencies was investigated, and the sensitivity of wave velocity to axial stress was quantified to determine an appropriate frequency pair. In addition, the influence of geometric factors, including bolt diameter and thread morphology, on guided-wave propagation was experimentally evaluated. Results indicated that although the linear relationship between TOF and axial stress was preserved under different geometrical configurations, the stress sensitivity coefficient varied with structural parameters. The effect of Poisson-induced radial contraction was further quantified and found to introduce negligible variation in group velocity within the engineering stress range. Experimental results demonstrated that the dual-frequency method exhibited a stable linear correlation with the TOF ratio and reduced the average measurement error from 6.88% to 3.43% compared with the single-frequency method. Furthermore, the proposed approach provides a theoretical foundation for error compensation in engineering applications.