Numerical solution of Rayleigh-Lamb frequency equation for real, imaginary and complex wavenumbers

¹ Department of Applied Mechanics, Faculty of Mechanical Engineering, VŠB-Technical University of Ostrava, 17. listopadu 15/2127, 708 33 Ostrava-Poruba, Czech Republic
² IT4Innovations National Supercomputing Center, VŠB-Technical University of Ostrava, Studentská 6231/1B, 708 33 Ostrava-Poruba, Czech Republic
³ Department of Control Systems and Instrumentation, Faculty of Mechanical Engineering, VŠB-Technical University of Ostrava, 17. listopadu 15/2127, 708 33 Ostrava-Poruba, Czech Republic

^* Corresponding author: michal.sofer@vsb.cz

Abstract

Guided waves, especially Lamb waves or shear-horizontal waves, are widely used types of waves for ultrasonic inspection of large structures. Well known property of guided waves is their dispersive character, which means that the propagation velocity of the particular wave mode is not only a function of physical properties of the material, in which the wave propagates or the wave´s frequency, but also depends on the geometry of the structure in itself. Dispersion curves provide us the information related to the dependency between the wavenumber and the frequency of the particular mode and can be obtained by a numerical solution of Rayleigh-Lamb frequency equation. A solution of Rayleigh-Lamb frequency equation forms for a given frequency and plate thickness a set of a finite number of real and pure imaginary wavenumbers and an infinite number of complex wavenumbers. Proposed paper presents a complete procedure of how to obtain all three kinds of wavenumbers for a given geometry and frequency interval. The main emphasis is placed on the effectiveness of the procedures, which are used for finding the roots of dispersion equation for all three kinds of wavenumbers.