Generalized analytic model for rotational and anisotropic metasolids

• Published in: Journal of physics communications Vol. 2; no. 3; p. 35035
• Main Authors: Favier, Elie, Nemati, Navid, Perrot, Camille, He, Qi-Chang
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 21.03.2018
• Subjects: acoustic metamaterials; Acoustics; effective density of moment of inertia; effective-medium parameters; elastic metamaterials; homogenization; Inertia; local resonances; Mechanics; Physics; rotational motions; low frequencies; homogenization; axial translation; effective-medium parameters; rotation; local resonances; elastic metamaterials; acoustic metamaterials; rotational motions; local resonance; effective density of moment of inertia; band gap
• ISSN: 2399-6528; 2399-6528
• DOI: 10.1088/2399-6528/aab5a5

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 . 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. As such, the effective density of moment of inertia is introduced to characterize the homogenized material with respect to its rotational mode. The results obtained by this analytical continuum approach are compared with those from discrete mass-spring model, and the validity of the latter 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 that are taken into account, i.e., axial translation for cylinders, and rotations for both cylindrical and spherical systems, can occur at lower frequencies compared with the previously studied plane-translational modes.