Wave propagation along transversely periodic structures

Abstract

The dispersion curves for guided waves have been of constant interest in the last decades, because they constitute the starting point for NDE ultrasonic applications. This paper presents an evolution of the semianalytical finite element method, and gives examples that illustrate new improvements and their importance for studying the propagation of waves along periodic structures of infinite width. Periodic boundary conditions are in fact used to model the infinite periodicity of the geometry in the direction normal to the direction of propagation. This method allows a complete investigation of the dispersion curves and of displacement/stress fields for guided modes in anisotropic and absorbing periodic structures. Among other examples, that of a grooved aluminum plate is theoretically and experimentally investigated, indicating the presence of specific and original guided modes.

Elastic waves guided by a welded joint in a plate

“…Since the derivation of the SAFE theory in solids has been detailed in previous research work (Predoi et al 2007), only the equations used in this paper will be briefly explained. The mathematical model of the SAFE method in solids is based on the three-dimensional elasticity approach.…”

“…in which all matrix coefficients are given by Predoi et al (2007). The nature of the solution is thus to find eigenvalues of wavenumber k for chosen values of angular frequency u.…”

High-temperature (>500°c) wall thickness monitoring using dry-coupled ultrasonic waveguide transducers

“…Rose [19] and Graff [20]) analytical solutions to wave propagation in infinite plates and perfectly cylindrical waveguides are usually presented, but solutions to waveguides of rectangular cross sections are more complex and are not presented. Solutions for rectangular cross section (strip) waveguides can be found using a semi analytical finite element technique (sometimes referred to as 'SAFE' [35]). The analysis is beyond the scope of this paper and was presented in a separate publication [36], but the main findings will be recalled here.…”

Feature guided waves (FGW) in fiber reinforced composite plates with 90° transverse bends

“…Modal studies for the bent plate with anisotropic properties were carried out by applying the well-known SAFE method [12]. It solves an eigenvalue problem of the solid with constant waveguides to find all possible propagation modes at a chosen frequency.…”