Investigation of guided wave dispersion characteristics for fundamental modes in an axisymmetric cylindrical waveguide using rooting strategy approach

Abstract

Guided wave propagation and its dispersion phenomenon in infinite solid elastic rods are encountered in several applications including, mechanical and civil engineering fields. A robust root finding method based on the Pad� approximation is presented for studying the dispersion characteristics of guided wave motion in a solid cylindrical rod with a circular cross-section. The theoretical analysis is conducted in the context of the theory of elasticity for deriving the simplified solution for the classic Pochhammer frequency equation. In this research work, dispersion curves of fundamental modes, namely, torsional (Formula presented.) longitudinal (Formula presented.) and flexural (Formula presented.) modes, are studied adequately. Based on the Pad� approximants, the solution strategy for the original Pochhammer frequency equation is improved. The calculation results herein show that this method is stable and efficient under the condition of guaranteeing an absolute wavenumber calculation accuracy, which can avoid the leakage of its close root in the curve. The dispersion curves obtained from the root-finding method by Pad� approximation are compared with the theoretical ones obtained by solving the corresponding Pochhammer frequency equation. It is observed that they coincide well with each other even in the region where the slope changes sharply, meaning that the proposed rooting strategy can be favorable for the rapid convergence of the theoretical solution. It is also extended to the solution of the wavenumber-frequency curve of the complex wavenumber domain in the viscoelastic waveguide. Henceforth, the proposed rooting approach can be employed to determine the dispersion characteristics of multiple modes in a cylindrical waveguide. � 2020 Taylor & Francis Group, LLC.