Spatial spectra of the eigenmodes of ribbed plates projected on dispersion branches

International audienceA vast literature has been devoted to the transverse vibration and the sound radiation of ribbedplates over the last decades. The present study has been motivated by the analysis of the dynamicalbehaviour of piano soundboards. As a rough approximation, a piano soundboard can beconsidered as an orthotropic ribbed plate. Our purpose is to establish condensed descriptionsfor their dynamics. For low frequencies, regularly ribbed plates can be considered as homogeneousplates. It is usually considered that homogenization is valid only up to a frequencycorresponding roughly to the confinement of one half wave-length between the (periodicallyspaced) ribs. Beyond that frequency, depending on the relative characteristic mobility of theribs and that of the base plate, the ribs may constrain transverse waves to be guided betweenthem. We focus here on the spatial spectrum of the normal modes of the ribbed plate (2DFourier transforms of the modal shapes). It appears that most of the peaks of each spectrumcan be seen as belonging to one of a few dispersion branches in an appropriate (w; k)-plane.Interestingly, different peaks of a spectrum (of one given mode) usually "belong" to differentdispersion branches. When valid, this description may prove an interesting intermediate step toderive approximations for the sound radiation of such plates