Experimental Observation of Cumulative Second-Harmonic Generation of Circumferential Guided Wave Propagation in a Circular Tube

Abstract

The experimental observation of cumulative second-harmonic generation of the primary circumferential guided wave propagation is reported. A pair of wedge transducers is used to generate the primary circumferential guided wave desired and to detect its fundamental-frequency and second-harmonic amplitudes on the outside surface of the circular tube. The amplitudes of the fundamental waves and the second harmonics of the circumferential guided wave propagation are measured for different separations between the two wedge transducers. At the driving frequency where the primary and the double-frequency circumferential guided waves have the same linear phase velocities, the clear second-harmonic signals can be observed. The quantitative relationships between the second-harmonic amplitudes and circumferential angle are analyzed. It is experimentally verified that the second harmonics of primary circumferential guided waves do have a cumulative growth effect with the circumferential angle.

Guided waves for damage identification in pipeline structures: A review

“…Using the nonlinear parameter, microstructure changes caused by different cycles of thermal fatigue in an aluminium pipe were evaluated experimentally with longitudinal fundamental wave excitation [108] and it is shown that the magnitude of the nonlinear parameter grew with thermal fatigue cycles, as shown in Figure 15. Another experimental study observed the accumulation of second harmonic as the circumferential angle θ increased with the excited circumferential wave in a tube, [109] as shown in Figure 16…”

“…[79] In the frequency spectrum, modulations can be seen at the sum and difference frequencies, which indicate the existing of nonlinearity. Furthermore, to locate the position of localised degradation in a pipe, tomographic scanning ) and the propagation distance under different thermal fatigue cycles [108] FIGURE 16 A 2 /A 1 2 versus circumferential angle θ at the driving frequency 0.88 MHz [109] FIGURE 17 Modulation of probe signal amplitude, when the probing signal is (a) vibration and (b) ultrasonic signal [110] method combined with mixing wave excitation was applied in another numerical study. [114] Experimental studies using impact-modulation method and a new vibro-modulation system to detect stress corrosion cracks [115] and fatigue cracks of a welded joint [113] in steel pipes were reported respectively.…”

Fatigue crack detection in pipes with multiple mode nonlinear guided waves

“…Moreover, the simulation method of material nonlinearity in plate structures can also be applied to pipe counterparts. Experiments concerning material nonlinearities in pipes 35,36 have also confirmed the phenomenon of cumulative second harmonic generation with longitudinal or circumferential wave excitation.…”

Influence of Change in Inner Layer Thickness of Composite Circular Tube on Second-Harmonic Generation by Primary Circumferential Ultrasonic Guided Wave Propagation

“…[18,19] However, it is difficult for the traditional linear CUGW to monitor minor change in material/structure of a circular tube. Based on the theoretical and experimental investigations of nonlinear effect of CUGW propagation in a single layer circular tube, [20,21] it has been experimentally validated that the minor change (early damage) in a tube material can be quantitatively assessed using the acoustic nonlinearity parameter for CUGW propagation. [22] In addition to minor change in the tube material itself, it can be expected that a minor change in geometrical parameter (e.g., inner layer thickness) may also obviously influence the efficiency of SHG of primary CUGW propagation.…”

“…1, within the second-order perturbation, the bulk driving force of double the fundamental frequency 𝐹 (𝑙) ] inside the composite circular tube, as well as the traction stress tensor of double the fundamental frequency 𝑃 (2𝜔) s = 𝑃 [𝑈 (𝑙) ] on the interfaces/surfaces of the composite circular tube, can be generated due to the convective nonlinearity and the inherent elastic nonlinearity of solid. [8,[20][21][22][23][24]28] According to the modal expansion approach, 𝐹 (2𝜔) b and 𝑃 (2𝜔) s are, respectively, assumed to be the bulk and surface sources for generation of a series of doublefrequency CUGW modes that constitute the secondharmonic field (denoted by 𝑈 (2𝜔,𝑙) (𝑟, 𝜃)) of the 𝑙th CUGW mode, namely, [8,[20][21][22][23][24]28]…”