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

Abstract

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.

Confluence Effect of Debris-Filled Damage and Temperature Variations on Guided-Wave Ultrasonic Testing (GWUT)

“…It is considered zero for a traction-free body condition. The solution to Equation ( 3) by the method of potential separation, as in [22], results in characteristics frequency equations of lamb wave grouped into two modes as in Equations ( 5) and (6). The terms of the equations are as expanded in Equations (7) through (9).…”

“…The peak of similarity. The matching index value is then converted into time of flight using Equation (22).…”

Partial Energy Transfer Model of Lamb Waves Scattering in Materially Isotropic Waveguides

“…In the next step, both methods, i.e., semi-analytical and hybrid approaches, were then used to evaluate the energy scattering coefficients for selected fractions of reflected or transmitted energy of A 0 mode in sub-waveguide 3. In the case of the semi-analytical approach, the analysis began with the identification of real, imaginary, and complex wavenumbers [45], including an additional refinement procedure based on the Newton-Raphson method, in which the complex wavenumbers have to be considered in the form of conjugate pairs [44]. Feng et al [46] proved that the best results are obtained when the number of wavenumbers corresponding to S modes NS is higher by one compared to the number of A modes NA, i.e., NS = NA + 1.…”

Application of Improved b-Value and Clustering Analysis for Structural Integrity Assessment of CFRP Specimen under Tensile Loading

“…The given method also supports localization of the Ae sources using an array of sensors, which is a significant benefit for many industrial applications, where we encounter thin-walled geometries. The plate-like character enables the transformation of the initial voluminal waves into rayleigh or Lamb guided waves [4,5], which exhibit dispersion [6,7] and thus the Ae signal processing methodology is an integral part of the measurement procedure.…”