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

Michele Ducceschi*, Sebastian Duran, Henna Tahvanainen, Ludovico Ausiello

*Corresponding author for this work

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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 work, the current method is effective with any choice of boundary conditions. Furthermore, the error function is linear in the elastic constants, which may be computed easily 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. Several 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.

Original languageEnglish
Article number109949
Number of pages13
JournalApplied Acoustics
Volume220
Early online date8 Mar 2024
DOIs
Publication statusPublished - 15 Apr 2024

Keywords

  • Guitar acoustics
  • Inverse methods
  • Least-square optimisation
  • Orthotropic plates
  • Young's modulus

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