Study on Mode Repulsion of Ultrasonic-Guided Waves in Pipe Bends

Abstract

The wave motion of guided waves in pipe bends is still veiled in some mystery, which hinders the application of guided-wave techniques in the inspection of pipelines with bends. Mode repulsion, which exists in the wavenumber versus frequency dispersion curves of guided waves in pipe bends, is an intriguing phenomenon deserving in depth study. The governing equation of wave motion in pipe bends, deduced by the semi-analytical finite element (SAFE) method, can be regarded as an eigenvalue problem. The eigenvalue derivatives, with respect to the wavenumber, are investigated to determine whether mode repulsion will occur or not. A term in the second derivative of the eigenvalue is identified to determine the mode repulsions. With respect to symmetry, it is found that mode repulsion only occurs between modes of one and the same type, such as symmetric or antisymmetric modes, and does not occur between modes of different type, like between symmetric and antisymmetric modes. A specific case of mode repulsion in a small-bore thin-walled pipe in the low-frequency range, where relatively fewer modes exist, is further studied, and the interactions between these modes are clarified. The evolutions of mode shapes before and after mode repulsion are further illustrated.