Modal Analysis of Guided Waves in a Bar with an Arbitrary Cross-section

Abstract

Ultrasonic wave packets propagate in the longitudinal direction by inputting low frequency ultrasonic into such bar-like structures as rails. This ultrasonic mode, called guided wave has become popular as a promising technique for rapid long-range nondestructive inspection for pipes and rails. In guided wave inspection, guided wave velocities (dispersion curves) and wave structures are firstly needed. Dispersion curves and wave structures can be analytically derived for such simple structures as plates and pipes, but not for bar-like structures with complex cross-section such as rails. Authors have developed calculation technique to obtain the dispersion curves and wave structures for such structures using a special finite element method called a semi-analytical finite element method in which dispersion curves and wave structures can be obtained as eigenvalues and eignvectors of an eigensystem. This study developed more accurate calculation technique for dispersion curves and wave structures using mirror relation of guided wave modes and an iteration method for solution of the eigen problem. And experimental studies for JIS 6 kg rail verify that dispersion curves and wave structures were obtained with sufficient accuracy for typical out-of-plain vibration modes. Wave structures were obtained by measuring waveforms at many points on the curved surface of a rail with a laser interferometer controlled by robot arms.