Design of low-frequency 1D phononic crystals harnessing compression–twist coupling effect with large deflection angle

Abstract

The properties of metamaterials depend on not only their constituents but also the intrinsic microstructures. Phononic crystals, as one type of metamaterials whose attributes dramatically rely on the microstructure, have exotic dynamic characteristics with myriad applications in acoustic and vibration engineering fields. This paper investigates a kind of 1D phononic crystals with compression–twist coupling effect that is a novel inertia amplification mechanism revealing coupled translational and rotational motions, by analytical and numerical methods. The widely-used coupling coefficient is first modified to adapt to a wider range of deflection angles from 10° to over 150°. Then mathematical dispersion relations are established for isotactic and syndiotactic configurations according to the diatomic spring-mass model. Parametric studies including the mass distribution, the deflection angle, and the inertia of moment are carried out for investigating the starting frequency and the bandwidth of the 1st bandgap. In the end, the results of frequency response function (FRF) show that a geometry-optimized phononic crystal exhibits good attenuation performance within the 1st bandgap.