Prestressed Soundboards: Analytical Approach Using Simple Systems Including Geometric Nonlinearity

Author： Mamou-Mani Adrien Frelat Joël Besnainou Charles

ISSN： 1610-1928

Source： Acta Acustica united with Acustica, Vol.95, Iss.5, 2009-09, pp. : 915-928

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Abstract

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.