[Paper Review] Nonlocal elastic metasurfaces: enabling broadband wave control via intentional nonlocality

Hongfei Zhu, Timothy Walsh+2 more|arXiv (Cornell University)|Feb 24, 2020

Metamaterials and Metasurfaces Applications56 references92 citations

TL;DR

This paper introduces intentional nonlocality in elastic metasurfaces by using engineered flexible connectors to create wavenumber-dependent coupling forces between distant unit cells, enabling fully passive, broadband wave control. Experimental and numerical validation demonstrates a 1 kHz operating bandwidth (24.69% relative bandwidth) over six times broader than conventional local designs, achieving effective broadband wave blocking via total internal reflection.

ABSTRACT

While elastic metasurfaces offer a remarkable and very effective approach to the subwalength control of stress waves, their use in practical applications is severely hindered by intrinsically narrow band performance. This work introduces the concept of intentional nonlocality as a fundamental mechanism to design passive elastic metasurfaces capable of an exceptionally broadband operating range. The nonlocal behavior is achieved by exploiting nonlocal forces, conceptually akin to long-range interactions in nonlocal material microstructures, between subsets of resonant unit cells forming the metasurface. These long-range forces are obtained via carefully crafted flexible elements whose specific geometry and local dynamics are designed to create remarkably complex transfer functions between multiple units. The resulting nonlocal coupling forces enable achieving phase gradient profiles that are function of the wavenumber of the incident wave.The identification of relevant design parameters and the assessment of their impact on performance are explored via a combination of semi-analytical and numerical models. The nonlocal metasurface concept is tested, both numerically and experimentally, by embedding a total-internal-reflection design in a thin plate waveguide. Results confirm the feasibility of the intentionally nonlocal design concept and its ability to achieve a fully passive and broadband wave control.

Motivation & Objective

• To overcome the intrinsic narrowband performance of conventional passive elastic metasurfaces based on local resonances.
• To develop a fundamentally new design paradigm using intentional nonlocality to extend the operating bandwidth.
• To enable fully passive, broadband wave control without relying on active components or complex control systems.
• To validate the concept experimentally in a thin plate waveguide using a total-internal-reflection-type metasurface.

Proposed method

• Designing nonlocal metasurfaces by introducing long-range coupling forces between distant resonant unit cells via specially engineered flexible connecting elements.
• Developing a semi-analytical transfer-matrix model to account for nonlocal coupling forces and predict dynamic behavior of nonlocal supercells.
• Using the model to identify key design parameters and assess their impact on wave control performance.
• Embedding the nonlocal metasurface in a thin plate waveguide for numerical simulation and experimental testing.
• Fabricating the structure using 3D printing with metalized connectors and gluing them onto resonating masses to realize the nonlocal links.
• Validating performance via scanning laser Doppler vibrometry under white noise excitation (3–6 kHz), measuring spatially averaged amplitude ratios before and after the metasurface.

Experimental results

Research questions

• RQ1 Can intentional nonlocality be engineered in elastic metasurfaces to achieve broadband wave control?
• RQ2 How do wavenumber-dependent coupling forces from nonlocal connections affect the phase gradient and wavefront manipulation?
• RQ3 What is the achievable bandwidth of a nonlocal elastic metasurface compared to its local counterpart?
• RQ4 Can a fully passive nonlocal design outperform active or locally resonant designs in terms of operating range and robustness?
• RQ5 To what extent do fabrication imperfections and material variability affect the experimental performance of nonlocal metasurfaces?

Key findings

• The nonlocal metasurface achieved a 1 kHz operating bandwidth (3.55–4.55 kHz) with a 24.69% relative bandwidth centered at 4.05 kHz, representing approximately six times the bandwidth of the local design.
• Experimental results showed a significant reduction in the spatially-averaged amplitude ratio after the metasurface, confirming broadband wave blocking in the target frequency range.
• Full-field experimental data revealed that vibrational energy was largely confined before the nonlocal metasurface, while the local design allowed nearly unimpeded transmission.
• The nonlocal design demonstrated a marked increase in operating range despite fabrication-induced deviations, such as frequency shifts and reduced bandwidth, due to 3D printing tolerances and assembly inaccuracies.
• Numerical and experimental results were in good qualitative agreement, validating the semi-analytical model and the effectiveness of the nonlocal coupling mechanism.
• The concept is general and extendable to other metasurface types beyond the total-internal-reflection configuration tested.