Joël Frelat

Numerical simulation of a piano soundboard under downbearing

A finite element model of a piano soundboard is used to study the effect of the strings tension (downbearing) on its vibration, considering the ribs, the bridges and the crown. The downbearing is modeled with the prestress theory. Prestress calculation with linear and nonlinear models including geometric rigidity are compared in terms of the modal frequencies. The effects of the downbearing in modal frequencies and mobility are investigated and the importance of the crown on these results is evaluated. A simple phenomenological law is exhibited, which characterizes the evolution of eigenfrequencies with downbearing, including the initial crown.

Prestressed Soundboards: Analytical Approach Using Simple Systems Including Geometric Nonlinearity

String instruments makers introduce prestresses on soundboards by adjusting the contact between the strings and the soundboard (downbearing). The effects of these prestresses on the vibration of the soundboard are investigated analytically, using a simple system of rods (one degree of freedom) and a buckled beam under the first two modes. For these two systems, we present successively the evolution of the eigenfrequencies and the nonlinear dynamical properties (phase diagrams, backbone curves). The two main results are 1) the second order evolution of the eigenfrequencies with prestresses are in agreement with a previous numerical simulation on a soundboard with the hypothesis of static large displacements and 2) the nonlinear dynamical properties of the system are modified by prestresses, and a prestressed soundboard working with large displacements seems to be technically possible.

Prestress effects on the eigenfrequencies of the soundboards: experimental results on a simplified string instrument.

This paper presents an experimental study of the effects of prestresses on the vibration behavior of string instruments. These prestresses are created by gluing ribs (crowning) and tensioning string (downbearing). The effects of these prestresses were previously studied numerically for a piano soundboard by Mamou-Mani et al. [J. Acoust. Soc. Am. 123, 2401-2406 (2008)] and analytically for simplified models by Mamou-Mani et al. [Acta Acust. Unit. Acust. 95, 915-926 (2009)]. In the present study, a specified test bench is designed, including a simplified soundboard (a rectangular plate), a bridge, and a single string. The plate is subjected to in-plane and transverse loads. Vibrational eigenmodes are identified using nearfield acoustical holography (NAH) measurement. The evolution of eigenfrequencies with these specific prestresses is studied. The results show the effectiveness of NAH for this purpose and a very good qualitative concordance with previous numerical and analytical calculus.

The jew's harp, experimental study and modeling

Under its archaic aspects jews harp is a musical instrument highly subtle. Indeed, a metal blade (or wooden) attached to a rigid frame put into vibration by the musician, and coupled to the buccal resonator allow nice tune. The skilt of the jews harp focuses on the conformations of this cavity whose function is to select the right components of the vibration to be amplify. In our study, we have modelled a playing technique which involves blowing during the blade vibrates. In the lake of breath, the spectre of sound produced by the blade is odd, i.e., it includes at first approximation odd components (n+1) multiple the fundamental. Whereas when the musician adds breath the spectrum turns into a spectrum containing all components of basic integer multiples (n). This work takes place in the context of studies of vibrating systems under prestress and loaded. In that case the load, and the prestress are generated by the musician breath by bending the blade On the other hand, experimental studies are compare ...