Parameters of violin plates and their influence on the plate modes

Abstract

Noncontact measuring methods and numerical calculations are used in a study of musical instruments. First, a simple method to determine the material parameters of a blank to a violin plate is presented. Eigenmodes of rectangular free–free violin wooden blanks are determined using optical nondestructive methods, Chladni patterns, or tapping. Assuming orthotropic material, the first three eigenmodes for such a blank are calculated using the finite element method (FEM). It is shown that the frequency of each eigenmode depends on separate elastic parameters. With this one variable dependence, it is a simple task to determine effective material parameters for quarter-cut standard wooden blanks when the frequencies and mass are known. Second, the violin maker’s problem with the influence of material and geometrical parameters on the vibration modes is investigated. Numerical models and corresponding real violin plates are made from the spruce and the maple blanks. Good agreement between calculated and experimentally obtained plate modes is found. Calculations with a 10% variation in each parameter are thereafter used to give information about the influence of overall plate thickness variation, of local thickness variations, of changes in arch-height, and of material parameters. Third, boundary conditions for the plates when glued to the ribs are examined in a pilot experiment.