Torsional Guided Waves for Simulation of the Pipeline Testing: Frequency Analysis of the Signals

Purpose Torsional guided waves are widely used in long-range ultrasonic testing (LRUT) of pipelines due to their favourable propagation characteristics and strong actuation capability. However, accurate modelling of torsional wave propagation in long pipelines assembled from welded segments remains challenging. Conventional finite element models require very fine spatial discretisation to represent wave phenomena and become computationally prohibitive for long inspection ranges, whereas simplified lumped-parameter torsional models fail to capture the broadband frequency characteristics of wave propagation. Methods In this work, a distributed-lumped modelling framework is developed for torsional guided-wave analysis in long pipelines. Each pipe segment is represented as a distributed-parameter torsional waveguide, while welded joints are modelled as lumped elements characterised by refraction factors. The Dynamic Stiffness Matrix Method (DSMM) is employed to derive exact frequency-domain expressions for angular displacement and angular velocity without spatial discretisation. By assembling the dynamic stiffness matrices of multiple segments and welds, a compact frequency-dependent system is obtained that is well suited to long-range inspection problems. Results The proposed approach is applied to a 100 m pipeline composed of welded 12 m pipe segments. Frequency response signatures are obtained for both uniform and non-uniform weld refraction factors and are compared with results from a lumped finite element torsional model. The lumped model collapses the response into a small number of global resonances and fails to reproduce the broadband spectral content observed with the distributed formulation. Conclusion The results demonstrate that the DSMM provides an efficient and physically realistic framework for predicting torsional guided-wave frequency signatures in long pipelines, offering a robust basis for baseline construction and frequency selection in LRUT applications.