Convergence study on ultrasonic guided wave propagation modes in an axisymmetric cylindrical waveguide

Abstract

Guided wave propagation and its dispersion phenomenon of infinite solid elastic rods are encountered in several applications including, mechanical and civil engineering fields. In this paper, the elastic stress wave propagation in the axisymmetric circular cross-section of a high strength steel wire with cylindrical waveguide is investigated using a semi-analytical finite element (SAFE) method. The error analyses are carried out on fundamental modes, namely, flexural longitudinal and torsional modes. The theoretical framework for finite element (FE) discretization is established for the cylindrical waveguide. A three-node triangular linear element is used for solving SAFE dispersion solutions such as the wavenumber-frequency curve, phase velocity, and group velocity curves. The convergence and accuracy of the method are analyzed by comparing it with the calculation results of the transcendental Pochhammer frequency equation, and the meshing criterion is proposed. The use of higher-order (quadratic) elements are proposed for lower computational burden and effective method for solving eigenvalue problems. The effect of using 6-node triangular quadratic elements in the SAFE method for improving frequency accuracy is discussed in a detailed manner by proposing the meshing criterion. The calculation accuracy of a quadratic element semi-analytical discretization exceeds that of a linear element discretization with four times its radial circumference. The statistical histograms are demonstrated to prove the results of the proposed semi-analytical discretization method which can be used for solving cylindrical waveguides.