Influences of the interfacial properties on second-harmonic generation by primary circumferential ultrasonic guided wave propagation in composite tube

The influences of the interfacial properties on second-harmonic generation by primary circumferential ultrasonic guided wave (CUGW) propagation in a composite tube are investigated in this paper.Within a second-order perturbation approximation,the nonlinear effect of primary CUGW propagation may be treated as a second-order perturbation to its linear response.Due to the interfacial spring model,the properties of interface between the inner and outer circular tubes constituting the composite tube are characterized by the normal and tangential interfacial stiffness values.According to the technique of modal expansion analysis for waveguide excitation,the second-harmonic field of primary CUGW propagation can be decomposed into a series of double frequency CUGW modes.It is found that changes of the interfacial properties of composite tube will obviously influence the efficiency of second-harmonic generation by primary CUGW propagation.Specifically,for a given composite tube with a perfect interface,an appropriate fundamental and double frequency CUGW mode pair that satisfies the phase velocity matching condition can be chosen to enable the double frequency CUGW mode generated by the primary CUGW propagation to accumulate along the circumferential direction,and an obvious second-harmonic signal of primary CUGW propagation to be observed.When the changes of the interfacial properties of composite tube (versus the perfect interface with infinite interfacial stiffnesses) take place,the effect of second-harmonic generation by primary CUGW propagation will be influenced in the following aspects.Firstly, the changes of the interfacial properties in the case of perfect interface may provide different acoustic fields for the primary CUGW.This will influence the magnitude of the modal expansion coefficient of double frequency CUGW mode generated,because both the second-order bulk forcing source (due to the double frequency bulk driving force) and the second-order surface/interface forcing source (due to the quadratic term of expression of the first Piola-Kirchhoff stress tensor) in the governing equation of the double frequency CUGW are both proportional to the squared amplitude of the primary CUGW.Secondly,the second-order surface/interface forcing source in the said governing equation is directly associated with the interfacial stiffnesses.This will also lead to the change of the magnitude of the modal expansion coefficient of double frequency CUGW mode when the change of interfacial stiffnesses takes place.Thirdly,the change of the interfacial stiffnesses will influence the dispersion relation of CUGW propagation.The phase velocity matching conditions for the fundamental and double frequency CUGW mode pair,which are satisfied originally in the case of perfect interface,may not now be satisfied.This will remarkably influence the efficiency of second-harmonic generation by the primary CUGW propagation.It is found that when there is a clear difference between the phase velocities of the fundamental and double frequency CUGW mode pair (caused by the changes in the interfacial stiffnesses),the double frequency CUGW mode generated may not have a cumulative effect along the circumferential direction.In this case,the efficiency of second-harmonic generation by primary CUGW propagation will become more and more weak.Theoretical analyses and numerical simulations performed both demonstrate that the effect of second-harmonic generation by primary CUGW propagation is very sensitive to changes in the interfacial properties of composite tube, and that it can be used to accurately characterize the interfacial properties in composite tube structures.