Analysis of Guided Wave Propagation in a Multi-Layered Structure in View of Structural Health Monitoring +
Footnote †: _Appl. Sci._**2019**, 9, 4600; doi:10.3390/app9214600  
[PERSON]  
1 Bundesanstalt fur Materialforschung und -prufung (BAM), 12205 Berlin, Germany; [EMAIL_ADDRESS] (J.B.); [EMAIL_ADDRESS] (J.F.) Chair of NDT and Quality Assurance (LZfPQ), Saarland University, 66125 Saarbruecken, Germany; [EMAIL_ADDRESS]  
[PERSON]  
1 Bundesanstalt fur Materialforschung und -prufung (BAM), 12205 Berlin, Germany; [EMAIL_ADDRESS] (J.B.); [EMAIL_ADDRESS] (J.F.) Chair of NDT and Quality Assurance (LZfPQ), Saarland University, 66125 Saarbruecken, Germany; [EMAIL_ADDRESS]  
[PERSON]  
2 The  
test procedure for this type of vessels does not exist and needs to be developed. Various approaches have been proposed to assess the current degradation state of COPVs. Destructive tests of some of the vessels running in parallel with vessels being in service were suggested in [14]. Another approach is acoustic emission monitoring for prediction of the residual lifetime of COPVs [11; 15]. Many researchers have been exploring an option of monitoring pressure vessels using integrated optical fibres with Bragg grating sensors [16; 17; 18; 19; 20]. Another promising approach is guided wave-based monitoring [10; 12; 21; 22; 23], which has several advantages when compared to alternative monitoring techniques. One of the advantages is that the approach is non-destructive and another is the approach's holistic character with respect to detection and localisation of damage. To examine different features of guided waves with respect to the limits of detectability of damage in a structure to be monitored, specifically also with regard to location when considering the hybrid material mentioned above, higher-order modes provide an interesting option to be explored. These modes, when considered over the whole thickness of the laminate, do not necessarily have smaller wavelengths but rather possess more complex mode shapes. This, in turn, may allow damage located in different depths to be found and differentiated. Due to dispersion and the multimodal character of GWs, development of a damage detection technique based on GWs requires careful numerical modelling such that a realistic analysis of wave propagation and mode-damage interaction can be performed. At first, a tool for calculation of dispersion curves and mode shapes is required. For this purpose, efficient approaches have been developed and applied to layered structures, e.g., the transfer matrix method [24], the discrete layer method [25], the semi-analytical finite element method [26; 27] and the scaled boundary finite element method (SBFEM) [28]. Based on these curves, appropriate modes can be identified and considered for further analysis. Next, a numerical tool for modelling the propagation of the chosen GW modes is required. Numerous methods have been applied to wave propagation problems such as finite differences [29], finite volumes [30; 31; 32], and finite element methods [11; 33], to just name a few. An extensive review of simulation methods for guided wave propagation analysis can be found in [34]. In general, each method has its advantages and disadvantages depending on the given problem, and there is no universal method suitable for solving every problem efficiently. In this article, the SBFEM is used to analyse GW propagation in a plate consisting of an isotropic aluminium layer bonded to an anisotropic laminate made of carbon fibre reinforced plastics (CFRP). Compared to other methods, the SBFEM does not require full discretisation, thus reducing the computational effort required significantly. It is suitable for calculation of dispersion curves, mode shapes and modelling of the GW propagation [28; 35; 36]. The dispersion curves are computed with the SBFEM by discretising the cross-section (e.g., the plate thickness) of an infinite domain using high-order elements, as shown as an example in Figure 1a.