Slow sound mode prediction and band structure calculation in 1D phononic crystal nanobeams using an artificial neural network.

Phononic crystals, which are artificial crystals formed by the periodic arrangement of materials with different elastic coefficients in space, can display modulated sound waves propagating within them. Similar to the natural crystals used in semiconductor research with electronic bandgaps, phononic crystals exhibit the characteristics of phononic bandgaps. A gap design can be utilized to create various resonant cavities, confining specific resonance modes within the defects of the structure. In studies on phononic crystals, phononic band structure diagrams are often used to investigate the variations in phononic bandgaps and elastic resonance modes. As the phononic band frequencies vary nonlinearly with the structural parameters, numerous calculations are required to analyze the gap or mode frequency shifts in phononic band structure diagrams. However, traditional calculation methods are time-consuming. Therefore, this study proposes the use of neural networks to replace the time-consuming calculation processes of traditional methods. Numerous band structure diagrams are initially obtained through the finite-element method and serve as the raw dataset, and a certain proportion of the data is randomly extracted from the dataset for neural network training. By treating each mode point in the band structure diagram as an independent data point, the training dataset for neural networks can be expanded from a small number to a large number of band structure diagrams. This study also introduces another network that effectively improves mode prediction accuracy by training neural networks to focus on specific modes. The proposed method effectively reduces the cost of repetitive calculations.