Piano soundboard vibro-acoustic modeling through decomposition on the basis of orthotropic simply supported unribbed plate modes

The piano soundboard is an orthotropic plate made of spruce, ribbed by multiple stiffeners, with a big additional beam, nearly in a perpendicular direction, the bridge. This complex structure has an essential role in the working of the instrument. Indeed, since strings' sections are too small to radiate by themselves, their vibrations are transmitted to the soundboard which radiates efficiently the sound. The vibro-acoustic models of such a structure are rare and mechanisms involved in piano acoustical radiation are not so easy to undertake. The aim of this study is to concentrate efforts on the modeling of the "radiator": the piano soundboard. In the present paper, focus will be done on the way to calculate the plate soundboard vibration, in the case of special orthotropy, where the ribs and the bridge are present. We develop here a quasi-analytical model of the piano soundboard vibro-acoustical behavior which allows us for example to estimate the sensitivity of rib spacing, or of the bridge on the modal shapes and radiation's indicators as radiated power, space average velocity and soundboard radiation factor through parametric studies.