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# Acoustic, elastic and thermal metamaterials III

## 16:40 Invited talk : Topological Phononic Crystal

### Zhaoju Yang, Baile Zhang

#### Nanyang Technological University (Singapore)

Topological photonics which study topological properties of photonic systems is emerging recently. However a similar method combining the topology and phononic crystals still remains elusive. Our work transfers the classic quantum Hall effect into a phononic crystal. The time-reversal symmetry of the phononic crystal is broken by introducing a circulating fluid flow in each unit cell. Topologically-protected edge states are demonstrated at the boundaries of the phononic crystal, being immune to backscattering from disorders.

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## 17:00 Invited talk : Localization of flexural waves in thin plates

### Patrick Sebbah (1),F. Feppon (2),A. Labbe (2),C. Gillot (2),A. Garelli (2),M. Ernoult (2),G. Lefebvre (1),M. Dubois (1),A. Gondel (1),S. Mayboroda (2),M. Filoche (2)

#### (1)Institut Langevin - ESPCI (France) , (2)Ecole Polytechnique (France)

We investigate flexural wave localization following two different routes. The first approach consists in structuring thin plates to force elastic energy in specific locations. We show that regions of localization can be predicted from the knowledge of the constraints imposed on the plate. Reciprocally, the inverse problem is solved and the positions of fixed points are found which force confinement in a predetermined region. The second approach is to introduce resonant scatterers to confine energy by multiple scattering.

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## 17:20 Invited talk : Locally resonant elastic metamaterials and seismic applications

### Andrea Colombi (1),P. Roux (2),S. Guenneau (3),R. V. Craster (1)

#### (1)Imperial College London (United Kingdom) , (2)Joseph Fourier University (France) , (3)Institut Fresnel (France)

Two applications of locally resonant elastic metamaterials are here presented. In the first one, we introduce a directional cloak that both protect from elastic waves and cancel the back scattering produced by an obstacle over a broad frequency band. In the second study we introduce the results from numerical simulations and actual seismic observations showing how locally resonant metamaterials can successfully control surface waves in a typical seismological context characterised by a semi infinite halfspace and forest-tree resonators.

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## 17:40 Invited talk : High Frequency Homogenization for Travelling Waves in Periodic Media

### Richard Craster (1),Davit Harutyunyan (2),Graeme W. Milton (2)

#### (1)Imperial College (United Kingdom) , (2)University of Utah (USA)

The effective equations governing the spatial and time modulations of travelling waves in periodic media are obtained using an extension of the high frequency homogenization approach of Craster, Kaplunov and Pichugin. The effective moduli entering these equations can be obtained by solving appropriate equations at the cell level.

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