Session: 16-01-01: Government Agency Student Poster Competition

Paper Number: 151014

151014 - Dynamics of Space-Time Modulated Bilayer Elastic Moire Structures 

This work investigates the interplay of two recent concepts in wave physics: space-time modulation of physical properties and bilayered moire lattices. Time modulated structures have unique wave propagation properties arising from breaking time reversal symmetry. These include asymmetric bandgaps that support one way or unidirectional propagating waves with potential applications as nonreciprocal wave-based devices. Similarly, moire structures comprise of two sheets of graphene stacked on top of each other and twisted by a small angle about the out-of-plane axes. At specific angles, periodic patterns form whose unit cell is larger than the underlying hexagonal lattice. They have shown novel properties like superconductivity and two-dimensional magnetism.  

Here, we investigate the dynamics of time-modulated elastic moire beam-based lattice-structures. We consider two identical hexagonal lattices separated by a small distance and coupled by interlayer springs. Each lattice comprises of an array of beams at the edges of the hexagons, while additional rigid masses are attached at the nodes. The two lattices are rotated or twisted by an angle 21.78 degrees about the out-of-plane axis. This rotation angle results in a periodic moiré lattice with the smallest area. It comprises of 14 nodes in each layer, making it feasible for fabrication and experiments. There are two nodal locations in each unit cell where the top and bottom layer nodes coincide. The two layers are then coupled by inter-layer axial springs at these two discrete locations in each unit cell.  

The beams are modeled using Euler-Bernoulli theory with the stiffness and mass matrices derived from standard isoparametric beam finite elements. In addition, torsional modes are also considered, as well as the coupling of bending and torsion arising from the hexagonal lattice configuration. Dispersion analyses reveal that Dirac cones in the uncoupled hexagonal lattices separate and two frequency bandgaps open. These bandgaps are separated by two isolated dispersion branches. Next, we investigate the effect of modulating the stiffness of the interlayer springs in space-time on the wave properties in the frequency range spanning the two bandgaps. A finite moire lattice structure in the shape of a hexagon is considered, with the bottom layer fixed at the corners. We consider various stiffness modulations resulting from appropriate rigid motions of the top plate, including periodic in space as well as azimuthal variation about the center of a finite lattice. Transient simulations are conducted using a Runge–Kutta solver to quantify the asymmetric nature of wave propagation for various strengths and frequencies of time modulation. Our results open avenues for novel wave shaping that are outside the reach of passive metamaterials.  

Presenting Author: Tamanna Akter Jui Texas A&M University

Presenting Author Biography: Tamanna Akter Jui is doing her PhD in ME at Kansas State University. Her research focus is architected metamaterial.

Authors:

Tamanna Akter Jui Texas A&M University
Raj Kumar Pal Texas A&M University