2D Energy channeling in the locally coupled acoustic metamaterials

Mechanical and acoustic metamaterials are engineered systems possessing selected material properties (which are typically anomalous) which are mainly affected by a unit-cell element structure rather than material composition. Dynamics of metamaterials is a subject of growing interest in various fields of applied physics and engineering such as electrical engineering, electromagnetics, solid state physics,  optoelectronics, material sciences, semiconductor engineering,  nanoscience and others. In the past few decades, acoustic metamaterials have driven a considerable attention for their unique, adaptive, material properties. Liu et al. first introduced the concept of a locally resonant metamaterials (LRSM). The LRSM is composed of inclusions of dense material shapes covered with a soft material, with the inclusions embedded in the matrix. The central advantage of LRSM over the typical acoustically absorptive metamaterials is in their ability to form the low-frequency band gaps. Some intriguing dynamical properties of this special class of metamaterials such as negative effective mass, negative refractive index have been revealed in the recent studies. In most of these works, the locally resonant sonic structures assumed a perfectly linear internal resonator. However, as is known, inclusion of nonlinear attachments may drastically change the dynamical properties of the locally resonant structure leading to the well-known phenomena such as targeted energy transfer, broadband energy absorption and more.
In this talk I'll present the analytical investigation of energy channeling phenomena emerging in the locally resonant unit-cell model comprising an outer mass incorporating internal rotator and subject to the 2D, nonlinear local potential. In the current study we mainly focus on the singular and regular multi-scale analysis of the intrinsic mechanisms of formation and bifurcations of the special type of non-stationary regimes, characterized by the massive, bidirectional energy transport between the axial and the lateral vibrations of the outer element controlled by the internal, rotational device as well as the regimes of the unidirectional energy transport. The devised analytical procedure is based on a singular and regular multi-scale analysis constructed for the two distinct asymptotic limits of high and low energy excitations, respectively. The basic question of possible coexistence of various stationary and non-stationary regimes as well as their local and global bifurcations is addressed via the reduction of the global flow on the slow invariant manifold (SIM) in the vicinity of the fundamental resonance. Interesting observations of energy channeling phenomena emerging in the 1D and the 2D inertialky coupled lattices will be presented.