Superposition model of mode shapes composed of travelling torsional guided waves excited by multiple circular transducer arrays in pipes

In pipe inspection using ultrasonic guided wave technique, the current commercial transmitters are designed for the unidirectional guided wave excitation using multiple circular piezoelectric transducers arrays in the axial direction. However, the source with many individual transducer elements in arrays has difficulty in achieving an axisymmetric loading perfectly for defect detection. Therefore, a quasi-axisymmetric wave is formed due to many undesired wave modes are launched instead of a pure axisymmetric wave at a given excitation frequency. In this paper, a realistic superposition model of axial multiple transducer arrays is proposed. The model has many potential applications; one example is investigating the source influence on the generated quasi-axisymmetric wave effect. The analytical model is employed to achieve the predictions for investigating a transmitter's influence for the unidirectional enhancement of torsional T(0,1) guided wave mode excitation in a pipe inspection system composing of three piezoelectric transducer ring arrays. The excitation function with variable power levels among transducers in arrays is also introduced. The predictive results using the analytical model for the distribution of circumferential displacement amplitudes over time are verified using the finite element method and a CLV-3D laser vibrometry measurement on a 219.1-mm-outer-diameter steel pipe without defect. A comparison between calculated and test results has been analysed quantitatively. The respective results are in good agreement. Thus, predictions for the superposed wavefield can be used to analyse the realistic characterisation of the excitation function in axial multiple transducer arrays. Additionally, a sensitivity analysis for part-circumferential crack detection using the quasi-axisymmetric torsional modes generated is also evaluated using finite element modelling.