Influences and sensitivities of design parameters on bandgap of three-dimensional phononic crystals

Phononic crystals as manufactured materials have particular property called bandgap to control elastic wave propagation. The geometric and material parameters have considerable effects on bandgap, but the sensitivities of these parameters to the starting and ending frequencies, and width of bandgap are not yet clear, especially for three-dimensional and three-component PCs. Thus, in this paper, the generation mechanism of bandgap, the influences and sensitivities of geometric and material features on bandgap characteristics are fully investigated according to the improved plane wave expansion method, Sobol’s sensitivity method, and artificial neural network. The results demonstrate that the artificial neural network prediction model with multiple hidden layers has good fitness, of which the coefficients of determination for the starting and ending frequencies are 0.9981 and 0.9982, respectively. The radius of the scatterer and the radius of the coating layer have the greatest influence, followed by the elastic modulus and Poisson’s ratio of the coating layer on the starting and ending frequencies. The radius of the scatterer and lattice constant have the biggest effect, followed by the elastic modulus and radius of the coating layer on the bandgap width.