A method to estimate the rectangular orthotropic plate elastic constants using least-squares and Chladni patterns

Abstract

A method to retrieve the elastic constants of rectangular wooden plates is presented, relying on the measurement of a set of eigenfrequencies and the identification of the corresponding mode shapes, and belonging to the more general category of non-destructive inverse parameter estimation methods. Compared to previous works, the current method is effective with any choice of boundary conditions. Furthermore, the error function is linear in the elastic constants, which are computed via a matrix inversion. This framework lends itself naturally to a physical interpretation of the results in terms of linear combinations of eigenmodes, yielding new sets of modes and associated combined mode shapes in which the elastic constants are completely uncoupled. A number of numerical benchmark tests and experimental cases are treated in detail, highlighting the reliability of the proposed methodology in cases of interest in acoustics and musical acoustics.