PSI - Issue 52

Feifei Ren et al. / Procedia Structural Integrity 52 (2024) 730–739 Author name / Structural Integrity Procedia 00 (2023) 000–000

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for monitoring the integrity of structures through the detection of impact damage Kessler et al. (2002); Mallet et al. (2004); Qing et al. (2019). PZTs have the properties of electromechanical coupling, lightweight, thermal stability, and resistance to high temperatures Mitra and Gopalakrishnan (2016). They can act as actuators and sensors, and be applied for damage detection in large-scale structures Ihn and Chang (2008). However, variations in environmental conditions can significantly impair the accuracy and reliability of GWSHM systems Salmanpour et al. (2017). Tem perature alterations have a direct impact on the wave propagation characteristics, resulting in variations in the group velocity of signals Lanza di Scalea and Salamone (2008). Consequently, it becomes imperative to incorporate tem perature compensation algorithms to e ff ectively mitigate these e ff ects Raghavan and Cesnik (2008); Konstantinidis et al. (2006). The e ff ect of temperature di ff erence has been studied extensively, including the e ff ectiveness of various temperature compensation methods Gorgin et al. (2020); Yue and Aliabadi (2020); Giannakeas et al. (2023). Considering the impact of temperature variations on the group velocity, the current state of research in this field still presents challenges. Lots of temperature compensation methods are predominantly based on experimental findings, and accurately quantifying the e ff ects of temperature on group velocity necessitates the collection of a substantial amount of baseline measurements across a wide temperature range, which proves impractical. This limitation presents an additional challenge when seeking to extend the temperature compensation method from one plate thickness to another, even if both plates are composed of the same material. The main objective of this research uptake by the aeronautical industry focused on the sensitivity analysis of the group velocity with the influence of temperature. The relationship of the group velocity, frequency and plate thickness is established based on the SAFE, which is used in there to calculate the dispersion curve Yue (2020), as it has the advantages of solving arbitrary cross-section waveguide problems, low computation cost, and less prone to missing roots in developing the dispersion curves Rose (2000). Followed by that, the temperature-dependent material properties are taken into account and their impact on the wave propagation characteristics are analyzed. By quantifying the sensitivity of the group velocity to temperature, it is found that the group velocity can be considered constant within a specific range of frequencies times thicknesses, which is referred to as the non-dispersive zone. In this region, variations in frequency and thickness do not significantly a ff ect the group velocity. By focusing on the non dispersive zone, the e ff ects of temperature on the group velocity can be compensated for composite panels with di ff erent thicknesses. This analysis helps in understanding the behavior of Lamb waves under varying temperature conditions and con tributes to the development of techniques for temperature compensation in guided wave-based applications. By un derstanding the sensitivity of group velocity to temperature changes, appropriate compensation techniques can be developed to account for temperature e ff ects and enhance the accuracy of measurements and interpretations. Overall, the sensitivity analysis of group velocity change with the influence of temperature enhances the knowledge of the temperature behavior of guided waves and contributes to the advancement of SHM techniques. The paper is structured as follows: Section 2 presents the methodology employed in this study. Section 3 discusses the temperature-dependent material properties that were investigated. The results and discussion are presented in Section 4, which includes an analysis of the temperature e ff ect on group velocity and the sensitivity analysis of group velocity change with temperature. Finally, Section 5 provides the conclusion of the study. The non-dispersive zone, where the group velocity remains constant, is of significant interest as it provides a reliable and predictable behavior of guided wave signals. By focusing on this zone, the sensitivity of the group velocity to temperature variations can be analyzed without the complicating e ff ects of dispersion. In order to evaluate the sensitivity of the temperature e ff ect on the group velocity, a comprehensive theoretical analysis is conducted first to examine the relationship between the group velocity, frequency, and panel thicknesses. In this section, the theoretical analysis of the dispersion curve is presented and the dispersion curves are calculated using the SAFE method. The SAFE method is selected for its exceptional computational stability and the inherent advantages it o ff ers through the combination of numerical finite element method (FEM) and analytical wave propagation formulations Giurgiutiu and Faisal Haider (2019). For a more detailed account of the dispersion curve can be found in references Huber (2021); Giannakeas et al. (2020). 2. Methodology