Transmission and Reflection Coefficients for Damage Identification in 1D Elements

Abstract

According to the latest research results presented in the literature changes in propagating waves are one of the most promising parameters for damage identification algorithms. Numerous publications describe methods of damage identification based on the analysis of signals reflected from damage. They also include complicated signal processing techniques. Such methods work well for damage localisation, but it is rather difficult to use them in order to estimate the size of damage. It is natural that propagating wave reflects from any structural discontinuity. The bigger the disturbance the bigger part of a propagating wave reflects from it. The amount of energy reflected and transmitted through any discontinuity can expressed as reflection and transmission coefficients. In the literature different application for these coefficients may be found – the most often cited application is connected with localising changes in the geometry of structures. Changes in the coefficients due to cross section variations in rods and beams or due to existence of stiffeners in plates are well documented. However there are no application of using the reflection and transmission coefficients for damage size identification. For this reason the analysis presented in this paper has been carried out. The article presents a method of damage identification in 1D elements based on the wave propagation phenomenon and changes in reflection and transmission coefficients. The changes in transmission and reflection coefficients for waves propagating in isotropic rods with different types of damage have been analysed. The rods have been modelled with the elementary, two and three mode theories or rods. For numerical modelling the Spectral Finite Element Method has been used. Several examples are given in the paper.

Assessment of flexural beam behaviour theories used for dynamics and wave propagation problems

“…For this reason an appropriate representation of these modes in a broad range of frequencies requires a greater number of terms of Maclaurin series, given by Eqs. (18), in order to capture the complexity of the interaction phenomena [32][33][34][35].…”

“…They are very well represented by the time-domain spectral element method or the spectral finite element method proposed by Patera [31]. The use of the spectral finite element method for investigation of propagation of elastic waves and wave-damage interaction in beam-like structures was presented and reported in [32][33][34][35] and the other branche of the time-domain methods are the methods that apply the wavelet transform in a similar manner as it takes place in the frequency-domain approach. In the case of dynamic problems related with beam-like structures they can be represented by [36][37][38].…”

Bayesian inference for damage identification based on analytical probabilistic model of scattering coefficient estimators and ultrafast wave scattering simulation scheme

“…The physical background behind this is given by the fact that elastic wave energy is transmitted, reflected and converted to different wave modes when impinging to a structural inhomogeneity. On that basis, it is possible to relate the damage extent or size to the acquired wave scattering properties [16].…”

Bayesian Damage Characterization Based on Probabilistic Model of Scattering Coefficients and Hybrid Wave Finite Element Model Scheme

“…Nowadays, ultrasonic GW-based SHM methodologies have been widely reported to be sensitive to small damage, convenient and efficient in detecting structural damage [3], such as fatigue cracks in metallic structures, debonding and delamination in composite structures. The scattered waves need to be analyzed using certain damage identification algorithms to extract various characteristics containing essential information about the damage [4,5]. Over the past decades, tremendous efforts have been directed to extract structural conditions using GWs.…”

“…By making full use of the Bayesian system identification framework for accommodating measurement noise and modeling errors properly, this study aims at formulating a generic methodology for probabilistic damage characterization based on wave scattering characteristics [4,5]. The scattering coefficients are probabilistically modelled by using absolute complex ratio random variables [10].…”