Abstract
Hierarchically structured phononic crystals are proposed for filtering multiple frequency bands. The advantages of using structural hierarchy come from its multiscale periodicity and the increased number of controllable parameters, which contribute to open multiple bandgaps in broadband frequency ranges and adjust the positions of those bandgaps. By deriving a transfer-matrix-based theoretical formula, hierarchical phononic crystals are designed that filter the frequency bands for randomly selected frequencies in the ultrasonic range of 20 kHz to 10 MHz. Their wave-filtering capability is demonstrated by using numerical simulations with consideration of material loss. By comparing the transmittance spectra of the hierarchical phononic crystals with those of conventional ones, the structural hierarchy of the former is shown to be advantageous in filtering multiple frequency bands.
Highlights
Structured phononic crystals are proposed for filtering multiple frequency bands
As well as designing hierarchical structures, we investigate the advantage of hierarchical PCs (HPCs) over conventional phononic crystals (PCs) in filtering multiple target frequency bands
By using a quantity defined as the filtering efficiency, which is a measure of whether one can achieve the desired wave-filtering capabilities by using HPCs or conventional PCs, we show that structural hierarchy is a key concept for handling wave problems and is not limited to solving static problems or thermodynamic problems
Summary
Structured phononic crystals are proposed for filtering multiple frequency bands. In thermodynamics, it was reported that using structural hierarchy in a honeycomb structure improved the heat resistance and thermal anisotropy, and those properties could be controlled by manipulating the geometrical parameters of the hierarchical structure[13] Another application of hierarchical structure that has been investigated is for opening broad acoustic and elastic bandgaps. Zhang and To14 investigated the wave-filtering capability of 1D hierarchical structures thoroughly for different hierarchy levels They reported that (i) the overall bandwidth covered by the bandgaps of PCs with hierarchy is much broader than that of the conventional PCs and (ii) using a higher level of hierarchy opens broad bandgaps in lower-frequency ranges. The ultimate goal of the present study is to find the optimal internal hierarchical structures for given geometrical constraints
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