Tunable bandgaps in soft phononic plates with spring-mass-like resonators

Abstract

Controlling band gaps of phononic crystals in real time through external stimuli (e.g. mechanical loadings, electric fields, and magnetic fields) shows potential applications in adaptive acoustic devices. It has been indicated that alteration of structural geometry or effective material properties due to external mechanical loadings will effectively change the bandgaps. In this regard, inducing significant post-buckling deformations in phononic crystals becomes an effective way to tune the band gaps. Few studies however have been reported to tune the band gaps through small deformations under which the geometry of phononic crystals is almost unchanged. In this work, a phononic crystal plate made of soft material with resonant units is proposed. Each resonant unit consists of a mass which is connected to the perforated plate by thin beams. Finite element method is employed to study the deformation and the dispersion behavior of such structure when subject to external mechanical loadings. Obvious complete band gaps are found to even exist in the intact structure without any mechanical loading. The evolution of band gaps under stretching is systematically revealed. Results show that remarkable tunability of bandgaps with small pre-stretch or extension is realized when strong resonance appears for some particular modes. The resonance frequency is mainly affected by the mass of the resonator and the stiffness of the connecting beams. In the proposed structure, the stiffness of the connecting beams can be substantially increased under a small pre-stretch. As a result, the resonance frequencies of resonant modes are increased, giving rise to a remarkable modification of the band gaps, while the geometry of the structure is nearly unchanged.