The interaction of cylindrically guided waves with discontinuities

The interaction of cylindrically guided waves with discontinuities in the geometry of the waveguide is a topic that has stimulated a great deal of interest. The reflected or transmitted signals are closely related to the geometric parameters of discontinuities in pipes. Therefore, it is believed that a discontinuity in a pipe can be identified and even characterized by analyzing the effects of its geometric parameters on the reflection or transmission signals. For example, Lowe et al. [7] reported that the mode conversion in reflection from an axisymmetric mode to flexural modes enables discrimination between axially symmetric reflectors such as circumferential welds and non-axially symmetric defects. Demma et al. [8] considered the amplitude of the reflected mode converted signal and concluded that it is possible to estimate the circumferential extent of a corrosion defect by evaluating the ratio between the flexural reflected component and the axisymmetric reflected component. However, due to the pyruvate dehydrogenase kinase and complexity of the discontinuities in pipes, the problem of identifying and characterizing the discontinuities has not been figured out yet. The research about the interaction of guided waves with different discontinuities is still ongoing.
In this study, an attempt is made at developing a relationship between the reflection of guided waves and the geometric characteristics of deformations in pipes. First of all in Section 3 the geometric characteristics of two typical types of dent models -single and double sided dents- are analyzed and their geometric parameters are defined. In Section 4, both types of dents with varying the geometrical profiles are mechanically simulated in hollow aluminum pipes and then experimental measurements are carried out, respectively. The experimental results are presented in Section 5, and the effect of the geometric characteristics and parameters of these dents on the reflected signals is analyzed.

Guided mode properties
The properties of guided wave modes in pipes are complicated, but they have also been well understood. Fig. 1 shows the group velocity dispersion curves over a frequency range of 0–500kHz for an aluminum pipe (16mm outer diameter and 1mm wall thickness). It is seen from Fig. 1 that there are three types of guided wave modes propagating in the axial direction of the pipe. The modes are labeled L(0, n), T(0, n) and F(m, n), respectively, referring to axisymmetric longitudinal, axisymmetric torsional and non-axisymmetric flexural modes [9]. The first index m indicates the order of harmonic variation of displacement and stresses around the circumference and the second index n is a counter variable. It is clear from Fig. 1 that multiple modes can potentially propagate at a given frequency and the modes are also generally dispersive (the velocity of a particular mode changes with frequency) so that the original wave packet is distorted as reduction travels along the pipe. This phenomenon makes interpretation of the signals difficult and also leads to low signal-to-noise ratio problems. For practical purposes, it is generally desirable to excite a single guided wave mode in a non-dispersive frequency region, and much of the considerable effort has been concentrated on this by many researchers [3,7].
The longitudinal L(0,2) guided wave is one of the most attractive modes to be used in practical pipe inspection. Previous studies and experimental experience [7,8] have shown that this mode has the following advantages: (1) Almost non-dispersive over a wide frequency band, for example, the frequency range 200–300kHz is a particularly attractive choice for the above-mentioned aluminum pipe, according to the dispersion curves shown in Fig. 1. (2) Fastest group velocity, it will be the first signal to arrive at the receiver and so can readily be separated by time domain gating. (3) Easier to be excited without producing flexural modes by applying uniform excitation over the circumference of the pipe. (4) Sensitive to both internal and external defects as its mode shape consists approximately uniform axial motion throughout the pipe wall, as shown in Fig. 2. Thus, the L(0,2) guided wave mode was selected in this study for pipe deformation assessment.