An Investigation of Reflection Coefficients of the T(0,1) Mode Guided Waves at Axisymmetric Defects and Inverse Problem Analyses for Estimations of Defect Shapes

Abstract

The frequency dependences of the reflection coefficients at gradual step-down axisymmetric defects were experimentally evaluated for the investigation of the reflection phenomena of the T(0,1) mode guided waves. Different frequency dependences were observed depending on the axial profile of the defect. A mathematical model using the characteristic acoustic impedance for calculating the reflection coefficients at axisymmetric defects was introduced. The reflection coefficients for the gradual step-down axisymmetric defects were confirmed to be in good agreement with the calculation results. By utilizing the mathematical model, a reflection mechanism was explained precisely and was verified. An inverse problem analysis for estimating the shape of an axisymmetric defect was also proposed based on the experimental reflection coefficients as a function of frequency together with the calculation model. Experimental verification of the proposed estimation method was performed using circular concave axisymmetric defects inside pipe specimens. The estimation results and accuracy were discussed in terms of the relation between the frequency range and the axial length of the defects.

A mathematical model of the Lamb wave reflection at a two-dimensional rectangular notch

“…Previous research has been published regarding reflection phenomena of the SH plate wave, [5][6][7] the Lamb wave [8][9] and the guided wave propagating in piping. [10][11][12][13] In all the research mentioned above, it has been confirmed that a simple and basic principle describing the reflection phenomena at a defect has consistently existed; that is to say, the reflection coefficient at a defect varies primarily due to the interference between the two signal groups generated in the defect. The first group is generated around the initial increasing region of the defect, where the phase of the signal is inverted.…”

“…Each signal group is formed by overlapping all the individual waves generated and reflected at all points along the propagation direction within the region. 13) Unless the length of each region is much longer than the wavelength, each signal group is formed under fairly positive interference among the individual waves. The final observed wave as a whole defect signal is obtained eventually as a mixture of the two signal groups whose phases are polar opposite to each other.…”

The Elastic Spiral Phase Pipe

“…Most commonly used in pipe inspection are the L(0, 2) and T (0, 1) modes, due to their ability to be efficiently excited and their dispersive properties [10,11,12,13]; the L(0, 2) mode has the highest phase velocity and is only weakly dispersive, whilst the T (0, 1) is non-dispersive across the whole frequency spectrum. These modes are sensitive to circumferential defects and had have much success in the field of non-destructive testing and evaluation [14,15,16,17]. Higher order torsional modes, e.g.…”

Guided wave tomography based on least-squares reverse-time migration

“…It clearly depends on the depth or severity of damage. 48,49 Harvesting the non-dispersive characteristic of shear-horizontal (SH) waves, 50,51 Wang and Hirose 52 inverted damage shapes using reflection coefficients of damage-scattered SH waves.…”