  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.
