However, for conventional systems of particles interacting via purely repulsive or Lennard-Jones(LJ)-like potentials, this disorder length scale is large. In this limit, the vibrational spectrum exhibits well defined phonon gaps that characterizes linear elasticity. Phononic band gaps are naturally present in all systems as long as their size is larger than their characteristic disorder length scale. As such, our approach serves not only as a standalone algorithm, but can also be used to generate precursors used in combination with the various existing optimization techniques to accentuate particular functionalities, while having the assurance of sizeable spectral gaps at the vicinity of a pre-determined frequency. Unlike existing strategies that depend on optimizing linear response or some secondary cost functions, this scheme robustly generates spectral gaps with no fine tuning of the elastic and topological properties. In this work, we present a numerical scheme capable of rapidly generating phononic spectral band gaps that dictate the robustness of programmable mechanical behavior in disordered elastic networks. Previous studies addressing phononic or acoustic band gaps in discrete elastic systems have largely focused on ordered or quasi-periodic systems, with far less attention paid to spectral gaps of disordered solids. This concern for the spectral architecture has motivated studies on the formation and tunability of band gaps in disordered photonic systems, that have recently also been incorporating hyperuniform point distributions that display peculiar behavior in Fourier space and their resulting structure factor. As such, understanding and controlling the properties of spectral gaps forms an important aspect to metamaterial design that goes beyond simply optimizing for the displacement field of the low frequency eigenmodes. To robustly implement these novel features in a sustained and controllable manner requires the existence of spectral band gaps that isolate the specific desired functionality of low energy excitations from the remainder of its spectrum that constitute noise to the intended response. In particular, recent phononic applications originating from these concepts include the design of auxetic materials with negative poisson ratio, allosteric inspired nano- or macro-scale levers capable of eliciting a targeted mechanical response at a distance, and the experimental realization of materials with negative effective stiffness.
From its collective contributions to bulk acoustic or sound attenuation properties, to the remarkable precision in conformational changes made available with the advent of directed mechanical response, these soft modes have offered an unprecedented level of control over the design of modern meta-materials due to its remarkable localization and topological properties. Low energy excitations of vibrational modes in disordered solids have been a subject of recent interest, for it presents an exciting approach to the construction of tunable meta-materials with a wide range of applications. Our approach is relevant to design and realization of gapped spectra in a variety of physical setups ranging from colloidal suspensions to 3D-printed elastic networks. Our proposed procedure exploits sticky potentials that have recently been shown to suppress the formation of soft modes, thus effectively recovering the linear elastic regime where band structures appear, at much shorter length scales than in conventional models of disordered solids. These gaps occur even in disordered polydisperse systems consisting of relatively few particles ( N ~ 10 2 − 10 3).
In this work, we present as an additional tool to the existing repertoire, a numerical scheme that rapidly generates sizeable spectral gaps in absence of any fine tuning of the network structure or elastic parameters. However, reliably producing these gaps often require a high degree of network specificity through complex control optimization procedures.
Spectral gaps in the vibrational modes of disordered solids are key design elements in the synthesis and control of phononic meta-materials that exhibit a plethora of novel elastic and mechanical properties.
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