Non-dimensional modal analysis of musical instrument plates

This work presents a framework for assessing whether a given set of measured modal shapes and frequencies can be reliably interpreted using a thin-plate model, in the context of inverse parameter estimation for musical instruments' plate-like components. While inverse modelling of vibroacoustic systems is commonly performed on a per-mode basis, little attention has been given to whether the underlying modal data conform to the assumptions of the selected model, most often based on Kirchhoff-Love plate theory. Here, we propose a non-dimensional, mode-by-mode comparison between computed and reference modal data and show that this provides a robust means of identifying deviations from thin-plate behaviour. Apart from the rectangular plate, the work is conducted on plates shaped like typical musical instrument soundboards. Modal shapes and frequencies are computed using thick-plate finite element methods, allowing for the inclusion of shear and rotatory inertia effects. A comparison with traditional dispersion relation-based criteria demonstrates that cutoff frequency arguments significantly overestimate the frequency range over which thin-plate theory remains predictive in the modal domain. A case study involving plates of varying thickness illustrates the utility of the method, particularly when used in conjunction with inverse identification routines.