Elastic field scattered by a resonator in an acoustic metamaterial
Résumé
Locally resonant sonic materials are artificially structured composites designed to exhibit negative effective mass density and/or elastic constants at frequencies below the Bragg band gap, giving rise to one or several forbidden bands in a frequency range where the elastic wavelength is much larger than a characteristic dimension of the resonator. In this work, we have investigated the propagation of Lamb waves in structures made either of an isolated resonant pillar or of a periodical array of resonant pillars deposited on a thin plate. The resonators and the plate are made of silicon and are designed to vibrate in the MHz range. These structures deserve special attention since pillars exhibit compressional resonant mode (monopolar) and bending resonant mode (dipolar) that may cause respectively negative modulus and negative mass density. We used a finite element method to calculate the frequencies and polarizations of the normal modes of the structure, as well as the scattering of an incident Lamb wave by the pillars. These computations are then compared to experimental data recorded using a laser ultrasonic technique that maps both the phase and the amplitude of the normal displacements at the surface of the sample, resulting from the propagation of the scattered wave. At low frequency, where homogenization theory applies, the pillars vibrate in quadrature with the exciting Lamb waves when they are excited at the frequency of their compressional resonance modes. If the frequency slightly departs from the resonance, the pillars vibrate out-of-phase with respect to the incident waves. This work is supported by the Agence Nationale de la Recherche and Direction Générale de l'Armement under the project Metactif, grant ANR-11-ASTR-015.