title: Control of elastic wave propagation in one-dimensional piezomagnetic phononic crystals.
abstract: Two ways of controlling the acoustic waves propagation by external inductance or capacitance in a one-dimensional (1-D) piezomagnetic phononic crystal are investigated. The structure is made of identical bars, constituted of a piezomagnetic material, surrounded by a coil and connected to an external impedance. A model of propagation of longitudinal elastic waves through the periodic structure is developed and the dispersion equation is obtained. Reflection and transmission coefficients are derived from a 2 × 2 transfer matrix formalism that also allows for the calculation of elastic effective parameters (density, Young modulus, speed of sound, impedance). The effect of shunting impedances is numerically investigated. The results reveal that a connected external inductance tunes the Bragg band gaps of the 1-D phononic crystal. When the elements are connected via a capacitance, a hybridization gap, due to the resonance of the LC circuit made of the piezomagnetic element and the capacitance, coexists with the Bragg band gap. The value of the external capacitance modifies the boundaries of both gaps. Calculation of the effective characteristics of the phononic crystal leads to an analysis of the physical mechanisms involved in the wave propagation. When periodically connected to external capacitances, a homogeneous piezomagnetic stack behaves as a dispersive tunable metamaterial.
authors.affiliation: Institut d'Électronique, de Micro-électronique et de Nanotechnologie, UMR CNRS 8520, ISEN Department, 41 Boulevard Vauban, 59046 Lille, France.
authors.forename: Marie-Fraise
authors.initials: MF
authors.lastname: Ponge
authors.affiliation: Institut d'Électronique, de Micro-électronique et de Nanotechnologie, UMR CNRS 8520, ISEN Department, 41 Boulevard Vauban, 59046 Lille, France.
authors.forename: Charles
authors.initials: C
authors.lastname: Croënne
authors.affiliation: Institut d'Électronique, de Micro-électronique et de Nanotechnologie, UMR CNRS 8520, Cité Scientifique, 59652 Villeneuve d'Ascq Cedex, France.
authors.forename: Jérôme O
authors.initials: JO
authors.lastname: Vasseur
authors.affiliation: International Associated Laboratory LEMAC: IEMN, UMR CNRS 8520, PRES Lille Nord de France, ECLille, 59652 Villeneuve d'Ascq, France.
authors.forename: Olivier
authors.initials: O
authors.lastname: Bou Matar
authors.affiliation: Institut d'Électronique, de Micro-électronique et de Nanotechnologie, UMR CNRS 8520, ISEN Department, 41 Boulevard Vauban, 59046 Lille, France.
authors.forename: Anne-Christine
authors.initials: AC
authors.lastname: Hladky-Hennion
authors.affiliation: Institut d'Électronique, de Micro-électronique et de Nanotechnologie, UMR CNRS 8520, ISEN Department, 41 Boulevard Vauban, 59046 Lille, France.
authors.forename: Bertrand
authors.initials: B
authors.lastname: Dubus