Enhancement effect of cumulative second-harmonic generation by closed propagation feature of circumferential guided waves

On the basis of second-order perturbation approximate and modal expansion approach,we investigate the enhancement effect of cumulative second-harmonic generation(SHG)of circumferential guided waves(CGWs)in a circular tube,which is inherently induced by the closed propagation feature of CGWs.An appropriate mode pair of primary-and double-frequency CGWs satisfying the phase velocity matching and nonzero energy flux is selected to ensure that the second harmonic generated by primary CGW propagation can accumulate along the circumference.Using a coherent superposition of multi-waves,a model of unidirectional CGW propagation is established for analyzing the enhancement effect of cumulative SHG of primary CGW mode selected.The theoretical analyses and numerical simulations performed directly demonstrate that the second harmonic generated does have a cumulative effect along the circumferential direction and the closed propagation feature of CGWs does enhance the magnitude of cumulative second harmonic generated.Potential applications of the enhancement effect of cumulative SHG of CGWs are considered and discussed.The theoretical analysis and numerical simulation perspective presented here yield an insight previously unavailable into the physical mechanism of the enhancement effect of cumulative SHG by closed propagation feature of CGWs in a circular tube.

Analysis of Second-Harmonic Generation of Low-Frequency Dilatational Lamb Waves in a Two-Layered Composite Plate

We analyze the effect of second-harmonic generation（SHG） of primary Lamb wave propagation in a two-layered composite plate, and then investigate the influence of interfacial properties on the said effect at low frequency. It is found that changes in the interfacial properties essentially affect the dispersion relation and then the maximum cumulative distance of the double-frequency Lamb wave generated. This will remarkably influence the efficiency of SHG. To overcome the complications arising from the inherent dispersion and multimode natures in analyzing the SHG effect of Lamb waves, the present work focuses on the analysis of the SHG effect of low-frequency dilatational Lamb wave propagation. Both the numerical analysis and finite element simulation indicate that the SHG effect of low-frequency dilatational Lamb wave propagation is found to be much more sensitive to changes in the interfacial properties than primary Lamb waves. The potential of using the SHG effect of low-frequency dilatational Lamb waves to characterize a minor change in the interfacial properties is analyzed.

Response features of nonlinear circumferential guided wave on early damage in inner layer of a composite circular tube

A theoretical model to analyze the nonlinear circumferential guided wave(CGW) propagation in a composite circular tube(CCT) is established. The response features of nonlinear CGWs to early damage [denoted by variations in third-order elastic constants(TOECs)] in an inner layer of CCT are investigated. On the basis of the modal expansion approach, the second-harmonic field of primary CGW propagation can be assumed to be a linear sum of a series of double-frequency CGW(DFCGW) modes. The quantitative relationship of DFCGW mode versus the relative changes in the inner layer TOECs is then investigated. It is found that the changes in the inner layer TOECs of CCT will obviously affect the driving source of DFCGW mode and its modal expansion coefficient, which is intrinsically able to influence the efficiency of cumulative second-harmonic generation(SHG) by primary CGW propagation. Theoretical analyses and numerical simulations demonstrate that the second harmonic of primary CGW is monotonic and very sensitive to the changes in the inner layer TOECs of CCT, while the linear properties of primary CGW propagation almost remain unchanged. Our results provide a potential application for accurately characterizing the level of early damage in the inner layer of CCT through the efficiency of cumulative SHG by primary CGW propagation.

Characterization of inner layer thickness change of a composite circular tube using nonlinear circumferential guided wave:A feasibility study

The feasibility of using the nonlinear effect of primary circumferential guided wave(CGW)propagation for characterizing the change of inner layer thickness of a composite circular tube(CCT)has been investigated.An appropriate mode pair of the fundamental and double-frequency CGWs(DFCGWs)has been selected to enable the second harmonics of primary wave mode in the given CCT to accumulate along the circumferential direction.When changes in the inner layer thickness(described as the equivalent inner layer thickness)take place,the corresponding nonlinear CGW measurements are conducted.It is found that there is a direct correlation between change of equivalent inner layer thickness of the CCT and the relative acoustic nonlinearity parameter(Δβ)measured with CGWs propagating through one full circumference,and that the effect of second-harmonic generation(SHG)is very sensitive to change in the inner layer thickness.The experimental result obtained demonstrates the feasibility for quantitatively assessing the change of equivalent inner layer thickness in CCTs using the effect of SHG by primary CGW propagation.