Influence of the interfacial properties on guided circumferential wave propagation in the circular tube structure

The mathematical expressions both of displacement and stress fields of circumferential wave propagation in circular tube structure with a weak interface are derived on condition that the interfacial properties between the two circular tubes are characterized by the interfacial spring model. Based on the said displacement and stress expressions derived, the dispersion equation of ultrasonic guided circumferential wave (UGCW) modes is formally presented by using the corresponding mechanical boundary conditions. According to the technique of modal expansion analysis for waveguide excitation, for a given excitation source used to generate circumferential wave in circular tube structure, the corresponding field of circumferential wave propagation can be decomposed into a series of UGCW modes. Using the reciprocity relations and mode orthogonality, the analytical expression of UGCW mode expansion coefficient is derived, which is closely related to the given excitation source for UGCW generation and the interfacial properties between the two tubes. The influences of change in the interfacial property on dispersion and acoustic field of the UGCW propagation are numerically analyzed. In the cases of perfect and sliding interfaces, for a given UGCW mode, the relative change rate of phase velocity is defined, and then its curve versus frequency is calculated, through which the specific frequency can be determined where the UGCW phase velocity appears to be most sensitive to the change in the interfacial property. For a given UGCW mode and driving frequency, it is numerically found that the displacement field on the outside surface of the circular tube structure changes sensitively and monotonically with change in interfacial property between the tubes. Clearly, through choosing the appropriate driving frequency and the mode of UGCW propagation, both the UGCW phase velocity and the displacement field on the outside surface of the circular tube structure will be monotonic and sensitive to change in interfacial property. It is expected that the results obtained in this paper will be of significance for accurately characterizing the interfacial properties of composite circular tube structures by using the UGCW technique.