Analysis of second-harmonic generation considering nonlinear mechanical properties on cylindrical interface

Abstract

Formulation based on the eigenfunction expansion is shown for second-harmonic generation simulations at a cylindrical interface. The displacement potentials of fundamental wave fields and second-harmonic fields are expressed as sums of eigenfunctions. The cylinder-matrix interface is assumed to be imperfect and modeled as a nonlinear spring interface for the purpose of considering roughness of the interface. Nonlinear equations in this model are dealt with the perturbation theory. The relational expression on the expansion coefficients of the fundamental waves and the second harmonics is shown. The results for the P wave incidence are demonstrated; although arbitrary incident wave field is available in the present method. As a result, both P and SV second harmonics are generated at the cylindrical interface. The numerical results for the directivity patterns of second harmonics are also given. The results show that the directivity patterns depend on the interfacial stiffness. Moreover the relationships between the interfacial stiffness and the ratio of stress in forward direction to backward direction are investigated in order to discuss the interfacial stiffness dependence in detail. The ratio significantly varies with the interfacial stiffness and the relationships are different by the frequency of the incident wave. Due to these characteristics, the ratio of stress in forward direction to backward direction can be useful for the evaluation of the interfacial stiffness. The influence of the ratio of the transverse stiffness to normal stiffness on the ratio of stress is also demonstrated. It is shown that the ratio of the interfacial stiffness has little effect on the ratio of stress.