Localization in the piano soundboard

International audienceThe soundboard is the complex plane structure that radiates the piano sound. We focus on its structural vibrations. The arrangement of the stiffeners (parallel bars) displays some disorder (height, separation distance) that has been shown responsible for the localization of the vibrations above a precise frequency (Ege 2013, JSV; Chaigne 2013, JASA) By means of a finite-element method, we investigate the localization properties of the eigenmodes of a simplified soundboard model. The localization occurs close to the band-edge of the first Brillouin zone, indicating the importance of a slightly disordered structure, similarly to photonic or phononic crystals with defects (John 1987, PRL). For structural parameters typical of a piano soundboard, this phenomenon seems to force the soundboard to remain in the subsonic regime in a very large frequency range. Moreover, by the adaptation of the theory of the localization landscape (Filoche 2012 PNAS), we compute a dual landscape (Lyra 2015 EPL) for the high-frequency modes of a stiffened orthotropic thin plate. This enables to predict the position of localized eigenmodes. [Work supported by the ANR grant ANR-14-CE07-0014.