Editorial: Application of periodic structure theory with finite element approach

Abstract

A periodic structure consists of repeating unit cells. Fromman-made multi-span bridges to naturally occurring atomic grids, periodic structures are present everywhere. Brillouin (1953) first used the wave propagationmethod to study the dynamics of periodic lattices. The ability of periodic configurations to create electronic bands in semiconductors and crystals is similar to the structural/acoustic bandgap of elastic media. Reinforced plate and shell structures are frequently used in a variety of structural applications, including bridges, ship hulls, decks, aircraft, and aerospace rocket/missile structures, which are examples of periodic structures. Mead (1996) presents a thorough overview of the available literature on the vibration analysis of periodic structures. In the areas of homogeneous/heterogeneous composite structures, waveguides, phononic crystals (PCs), acoustic/elastic metamaterials, vibration acoustic isolation, noise suppression devices, vibration control, directed energy flow, etc., this might result in great implementations. Periodic structures are also used to study the tunability (Zheng et al., 2019) of filter characteristics, such as required acoustic band gap, propagation, cut-off frequency, attenuation, and response direction. Health monitoring (Groth et al., 2020) and damage detection of these structures requires a good understanding of the propagation of elastic waves through such periodic structures. In particular, the effect of periodicity on the movement of electromagnetic waves (Pierre, 2010) has been extensively studied and they have been applied to many optical and electromagnetic devices (Bostrom, 1983). The finite element (FE) theory-based numerical approach exhibits the most diversity and usefulness in modeling physical structures among the various numerical approaches. The theory of wave propagation in the periodic structure with FEM (PSFEM) is the goal of the study topic, and the numerical solution is based on the FE analysis of the unit cell of the structure. This numerical FE method enables high accuracy with very little computational effort and is a recommended option for predicting waves in one-dimensional and twodimensional single waveguides (Orris and Petyt, 1974; Pany et al., 2002; Pany and Parthan, 2003a; Pany et al., 2003; Pany and Parthan, 2003b; Pany, 2022). The majority of published OPEN ACCESS