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.