Multiple target frequencies filtering by using phononic crystals with structural hierarchy

We propose hierarchically structured phononic crystals for filtering multiple target frequencies with bandwidths. Structural hierarchy has geometrical characteristics of increased number of controllable parameters and multiscale periodicity, so that we can realize the multiple broad bandgaps and control the position of those bandgaps. We design the hierarchical phononic crystals that filter the frequency bands with randomly selected center frequencies in audible frequency range and demonstrate their wave filtering performances via numerical simulations with material losses considered. The filtering efficiencies of the conventional phononic crystals and the hierarchical ones are evaluated to higlight that hierarchical ones show better performance in filtering multiple frequencies that could not be filtered by conventional ones as the number of target frequencies increases.