Session: Research Posters

Paper Number: 114284

114284 - Observation of Localized Modes in the Continuum-Based Waveguides in Architected Elastic Plates 

We experimentally demonstrate the existence of a novel class of localized modes, namely bound modes in the continuum (BICs) in one dimensional and hinge localized modes in two dimensional architected elastic structures. BICs have the unique properties that their frequencies lie in the passband and their amplitude goes to zeros outside a compact region, thus zero leakage to surrounding.

 

To achieve BICs in one dimensional beam structure, we consider an array of periodic masses are attached to a rectangular beam. The key idea is to cancel shear force, bending moment and torsional moment outside a compact region, so the deformation is localized within this region. To execute the idea, carefully engineered side beams are added to our considered beam structure maintaining reflection symmetry. The side beams are designed using Euler-Bernoulli beam theory in such a way that their symmetric displacement field can nullify the forces outside the compact region. We theoretically show that a family of BICs are achieved for different dimensions and location of side beams, followed by an experimental demonstration of BICs in the beam structure. The theoretical predictions are complemented using finite element simulations with COMSOL software. For experimental demonstration, the beam was laser cut from an acrylic sheet and rigid masses are attached to the beam at periodic intervals. The beam is excited by a shaker and the velocity field was along the axis of the beam is measured using a Laser Doppler vibrometer. The experimental wave field also shows the excitation is confined in the compact region of the beam structure at the BIC frequency, thereby validating our proposed concept.

 

Next, we extended this concept to achieve localized modes in the continuum in two dimensional elastic structures. Inspired by lattice designs in quantum mechanics, we considered a square lattice of alternating out of plane stiffness in both directions. Our calculations indicate the existence of topological corner localized modes due to chiral and 2-fold rotation symmetry. We designed an elastic structure with each unit cell consisting of four nodes having rigid masses. The alternating stiffness values are achieved by varying the length and exploiting the observation that the stiffness scales inversely with the third power of length. Our finite element  simulations confirm the presence of corner localized modes in these elastic plates, both at a boundary and at a junction between four lattices. These lattices are copies of each other translated by a fraction of the unit cell length. Stacking an array of such junctions leads to a set of localized modes confined to this array. Our numerical and experimental results show waveguiding along a channel made of such an array. Notably, this waveguiding takes place in the passband and thus eliminates the need for a bandgap. Our results open avenues for novel devices that require elastic wave guiding and steering.

Presenting Author: Adib Rahman Kansas State University

Presenting Author Biography: Adib Rahman completed his bachelor's degree in mechanical engineering from Bangladesh University of Engineering and Technology (BUET), Bangladesh in 2019. Then, he started pursuing PhD in mechanical engineering at Kansas State University, USA from 2021. His research focuses on elastic metamaterial to achieve localized modes in different architected structure. During his undergraduate studies, he grew interest in computational mechanics that led him to PhD research.

Authors:

Adib Rahman Kansas State University
Sean Perkins Kansas State University
Raj Kumar Pal Kansas State University