Optimal absorption of flexural energy in thin plates by critically coupling a locally resonant grating

Abstract

The optimal absorption of flexural energy by the critical coupling of a locally resonant grating embedded in a thin plate is reported in this work for the reflection and transmission problems. The grating is made of a 1D-periodic array of local resonators. A viscoelastic coating is also placed on top of each resonator to control the intrinsic losses of the system. The scattering matrices for the propagative waves of both problems are obtained by means of the Layered Multiple Scattering Theory and validated by the Finite Element Method. In this work, we find that the perfect absorption can be obtained in the reflection problem and the maximal absorption in the transmission problem is limited to 50% by tuning the losses only. These results agree with the theoretical predictions since the eigenvalues reduce to the reflection coefficient in the reflection problem and only one of the two eigenvalues of the scattering matrix is critically coupled in the transmission problem. These results highlight the adaptability of the critical coupling method to optimize the absorption of locally resonant materials for flexural waves in 2D transmission and reflection problems, and pave the way to the design of resonators for efficient flexural wave absorption.

Keywords:

• Flexural Waves
• Perfect Absorption
• Multiple Scattering
• Metamaterials
• Critical Coupling

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work has been funded by the RFI Le Mans Acoustique (Région Pays de la Loire) within the framework of the MetaplaQ project. This article is based upon work from COST action DENORMS CA 15125, supported by COST (European Cooperation in Science and Technology). This work was partly supported by the project HYPERMETA funded under the program Étoiles Montantes de la Région Pays de la Loire and by the project eTNAA ANR-17-CE08-0035-01 (projet ANR 2017-2021). The authors also acknowledge support from the Spanish Ministry of Economy and Innovation (MINECO) and European Union FEDER through project PID2019-109175GB-C22.