Dispersion characteristics of arc-axis waveguides

Abstract

Ultrasonic single mode excitation methods, mode separation algorithms and damage detection applications all require the calculation of the dispersion characteristics of the waveguide. However, existing dispersion calculation methods are mainly applicable to straight-axis waveguides. Therefore, in this paper, a novel semi-analytical finite element method in cylindrical coordinates (SAFEM-CC) is established and we focus on the dispersion characteristics of arc-axis waveguides. The cross-section of the waveguide can have arbitrary complex shapes, and the correctness of this method is verified by the finite element eigenfrequency method. At the same time, this paper takes the example of an arc-axis structure with a square cross-section and investigates the convergence of SAFEM-CC under different numbers of elements, element types, and element orders. This paper also establishes a finite element simulation model to study the waveform transmission law over a wide frequency range and the wave amplitude distribution law within the cross-section of arc-axis waveguides. The dispersion characteristics of arc-axis waveguides at different radii are also investigated. Finally, the correctness of the proposed method and the dispersion characteristics of arc-axis waveguides are verified by a large number of experiments. The main conclusions are as follows: the waveform transmission laws of the guided wave in arc-axis waveguides at each frequency agree with the dispersion curve; the theoretical wavestructure gives the distribution law of the amplitude within the cross-section; when the axis is arc, the displacement of the wavestructure on the inner and outer sides does not have symmetry, and the difference between the left and right sides gradually increases as the radius decreases.