Experimental proof of emergent subharmonic attenuation zones in a nonlinear locally resonant metamaterial

Abstract

High-performance locally resonant metamaterials represent the next frontier in materials technology due to their extraordinary properties obtained through materials design, enabling a variety of potential applications. the most exceptional feature of locally resonant metamaterials is the subwavelength size of their unit cells, which allows to overcome the limits in wave focusing, imaging and sound/vibration isolation. To respond to the fast evolution of these artificial materials and the increasing need for advanced and exceptional properties, the emergence of a new mechanism for wave mitigation and control consisting in a nonlinear interaction between propagating and evanescent waves has recently been theoretically demonstrated. Here, we present the experimental proof of this phenomenon: the appearance of a subharmonic transmission attenuation zone due to energy exchange induced by autoparametric resonance. these results pave the path to a new generation of nonlinear locally resonant metamaterials. Metamaterials 1, 2 are artificially engineered materials designed to obtain specific, often exotic, properties. Among the wide variety of possible metamaterial properties, the opening of a band gap, which is defined as the frequency range where elasto-acoustic waves cannot propagate, is attracting increasing interest because of its versatile applications 3-5. In particular, a wide and low frequency band gap offers a number of potential applications, such as sound attenuation, super-resolution acoustic imaging, and vibration mitigation. Typical physical phenomena responsible for the band gap opening are Bragg scattering 6,7 , inherent to periodic structures, and local resonance 8 that also promotes band gaps in materials composed of unit cells with subwavelength dimensions. The latter is the focus of the present work. Locally resonant metamaterials operating in the nonlinear regime 9-11 provide even more opportunities for breakthrough applications. Recently, nonlinearities have been exploited in locally resonant granular crystals 12,13 or to obtain logic gates 14 and acoustic diodes 15. Despite of great interest, the number of investigations carried out on the nonlinear dynamic behavior of locally resonant metamaterials exhibiting attenuation frequency ranges is quite limited in comparison with linear ones, also because of the conceptual and modelling difficulties 16-20. Only few works investigated the energy transfer mechanisms induced by the nonlinear coupling between the resonator and the host medium. In some papers 21-24 , the irreversible energy transfer mechanisms are induced by a single purely nonlinear attachment, the so-called nonlinear energy sinks (NES). Only very few papers have considered cases in which nonlinear resonant attachments are densely or periodically distributed in a host material. In this case, two main energy transfer mechanisms can arise. The first one is called inter/intra-modal tunneling and is a well-studied phenomenon in nonlinear wave dynamics. It consists of an energy exchange between t...

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