Enabling novel dispersion and topological characteristics in mechanical lattices via stable negative inertial coupling

Abstract

Mechanical topological insulators have enabled a myriad of unprecedented characteristics that are otherwise not conceivable in traditional periodic structures. While rich in dynamics, new developments in the domain of mechanical topological systems are hindered by their inherent inability to exhibit negative elastic or inertial couplings owing to the inevitable loss of dynamical stability. The aim of this paper is, therefore, to remedy this challenge by introducing a class of architected inertial metamaterials (AIMs) as a platform for designing mechanical lattices with novel topological and dispersion traits. We show that carefully coupling elastically supported masses via moment-free rigid linkages invokes a dynamically stable negative inertial coupling, which is essential for topological classes in need of such negative interconnection. The potential of the proposed AIMs is demonstrated via three examples: (i) a mechanical analogue of Majorana edge states, (ii) a square diatomic AIM that can sustain the quantum valley Hall effect (classically arising in hexagonal lattices), and (iii) a square tetratomic AIM with topological corner modes. We envision that the presented framework will pave the way for a plethora of robust topological mechanical systems.

Tunable topological interface states in one-dimensional inerter-based locally resonant lattices with damping

“…A comprehensive study by Al Ba'ba'a et al [42] explored the effect of inertance on both dispersion and topological characteristics of 1D and 2D architected inertial metamaterials (AIM). Special attention was devoted to ideal and linearized inerter-based infinite monoatomic AIM representing the lockable rigid slider system with tunable angle θ.…”

“…Topological properties of inerter-based lattices are less explored in the literature. In recent work [42], a new class of architected inertial metamaterials was suggested for 1D and 2D mechanical lattice design with novel topological and dispersion characteristics. However, most of the studies apply ideal inerter elements to represent the inertia amplification effect in mechanical systems.…”

Inerter-controlled topological interface states in locally resonant lattices with beyond-nearest neighbor coupling

“…26,27 Unique wave propagation and topological properties were obtained in a onedimensional phononic-like periodic lattice through a passive mechanical component named inerter. 28 In recent years, mechanical inerter devices 29 have been widely exploited by both scientific and engineering communities. 30 In Ref.…”

Duality of Topological Edge States in a Mechanical Kitaev Chain

“…Although mechanical analogues of the Kitaev chain have been investigated in the past [13,[22][23][24], this is the first time that a system with an intrinsic particlehole symmetry that maps to a non-zero chemical potential Kitaev chain is presented. Furthermore, we find that this system supports a hitherto unobserved duality between the finite lattices with fixed and free boundary conditions.…”