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A method to retrieve the elastic constants of rectangular wooden plates ispresented, relying on the measurement of a set of eigenfrequencies and theidentification of the corresponding mode shapes, and belonging to the moregeneral category of non-destructive inverse parameter estimation methods.Compared to previous works, the current method is effective with any choice ofboundary conditions. Furthermore, the error function is linear in the elasticconstants, which are computed via a matrix inversion. This framework lendsitself naturally to a physical interpretation of the results in terms of linearcombinations of eigenmodes, yielding new sets of modes and associated combinedmode shapes in which the elastic constants are completely uncoupled. A numberof numerical benchmark tests and experimental cases are treated in detail,highlighting the reliability of the proposed methodology in cases of interestin acoustics and musical acoustics.

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