Editorial: Application of periodic structure theory with finite element approach

A periodic structure consists of repeating unit cells. From man-made multi-span bridges to naturally occurring atomic grids, periodic structures are present everywhere. Brillouin (1953) first used the wave propagation method 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).