Session: 01-02-01: Topological Phononics

Paper Number: 147420

147420 - Bulk to Localized Mode Transition in Elastic Plate Meta-Structures 

Wave localization has been extensively studied for over a century in various physical domains, including electromagnetism, elasticity and acoustics. In particular, the fundamental interplay between local properties (material composition and geometrical architecture) and structural defects has been proven to lead to the emergence of localized modes offering intriguing possibilities for spatial wave control. However, despite the variety of designs proposed so far, most of the approaches derive from contextual modifications that do not translate into a design paradigm due to the lack of a general theory. Few exceptions include designs endowed with topological dispersion bands, which, however, require changes over substantial portions of the structure.

To overcome these limitations, here we introduce a new rationale based on fractional of mode density in a bulk band to achieve localized modes in continuous elastic media. We first theoretically predict and experimentally demonstrate the spectral flow of a localized mode across a bulk frequency gap by modulating a single structural parameter at any chosen location in the structure. Our theoretical predictions are complemented by experimental demonstration with a family of 3D printed structures. In these structures, the diameter of beam segments connecting adjacent masses is varied periodically so that the resulting unit cell has three effective degrees of freedom for out of plane bending. Experiments are conducted exciting the structures with a shaker and measuring the velocity field with laser Doppler vibrometer. Our results clearly show the spectral flow of a localized mode across the entire bandgap, establishing the validity of the proposed concept.

We then use this concept to design an architected plate comprising of an array of coupled beams. The diameters of segments connecting adjacent masses in each of these beams smoothly transition across the array from being equal at one end to that corresponding to the design supporting localized mode at the other end. Three-dimensional finite element simulations confirm the existence of a mode which is thus a bulk mode at one end and a localized mode at the other end. Since the localized mode has a topological origin, its existence is immune to defects and manufacturing imperfections. The accompanying experiments are again conducted by fabricating a structure by 3D printing and exciting the structure with a shaker. The results illustrate how we can excite a localized mode by sending a bulk wave from the far field.  The simplicity and generality of the proposed approach opens new avenues in designing wave-based devices for energy localization and control.

Presenting Author: Raj Kumar Pal Kansas State University

Presenting Author Biography: Raj Kumar Pal is an Assistant Professor in the Department of Mechanical and Nuclear Engineering at Kansas State University. His research interests are in the static and dynamic behavior of elastic meta-structures.

Authors:

Svetlana Kuznetsova Institut d’Electronique de Micro ́electronique et de Nanotechnologie
Marco Miniaci Institut d’Electronique de Micro ́electronique et de Nanotechnologie
Raj Kumar Pal Kansas State University