Generalized analytic model for rotational and anisotropic metasolids

TL;DR

This paper develops a comprehensive analytical model for anisotropic and rotational metasolids, revealing negative effective densities and moments of inertia near resonances, and compares these results with discrete models.

Contribution

It introduces a generalized analytical approach for modeling anisotropic and rotational effects in metasolids, extending previous models and analyzing resonance behaviors.

Findings

Metasolids exhibit negative mass densities near translational resonances.

Negative density of moment of inertia occurs near rotational resonances.

Additional modes can resonate at lower frequencies than previously studied modes.

Abstract

An analytical approach is presented to model a metasolid accounting for anisotropic effects and rotational mode. The metasolid is made of either cylindrical or spherical hard inclusions embedded in a stiff matrix via soft claddings, and the analytical approach to study the composite material is a generalization of the method introduced by Liu \textit{et al.} [Phys. Rev. B, 71, 014103 (2005)]. It is shown that such a metasolid exhibits negative mass densities near the translational-mode resonances, and negative density of moment of inertia near the rotational resonances. The results obtained by this analytical and continuum approach are compared with those from discrete mass-spring model, and the validity of the later is discussed. Based on derived analytical expressions, we study how different resonance frequencies associated with different modes vary and are placed with respect to each other, in function of the mechanical properties of the coating layer. We demonstrate that the resonances associated with additional modes taken into account, that is, axial translation for cylinders, and rotations for both cylindrical and spherical systems, can occur at lower frequencies compared to the previously studied plane-translational modes.