Estimation of mechanical properties of panels based on modal density and mean mobility measurements

• We estimate Young's modulus, mass density, and modal loss factors of flat panels.
• The method requires affordable tools and a protocol suitable for a daily practice in an artisan's workshop.
• The method for estimating the modal density is valid as long as the modal overlap does not exceed 1.
• The Young's modulus and the mass density are estimated with a small error, from a few measurement points.

The mechanical characteristics of wood panels used by instrument makers are related to numerous factors, including the nature of the wood or characteristic of the wood sample (direction of fibers, micro-structure nature). This leads to variations in Young's modulus, the mass density, and the damping coefficients. Existing methods for estimating these parameters are not suitable for instrument makers, mainly because of the need of expensive experimental setups, or complicated protocols, which are not adapted to a daily practice in a workshop. In this paper, a method for estimating Young's modulus, the mass density, and the modal loss factors of flat panels, requiring a few measurement points and an affordable experimental setup, is presented. It is based on the estimation of two characteristic quantities: the modal density and the mean mobility. The modal density is computed from the values of the modal frequencies estimated by the subspace method ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques), associated with the signal enumeration technique ESTER (ESTimation of ERror). This modal identification technique is proved to be robust in the low- and the mid-frequency domains, i.e. when the modal overlap factor does not exceed 1. The estimation of the modal parameters also enables the computation of the modal loss factor in the low- and the mid-frequency domains. An experimental fit with the theoretical expressions for the modal density and the mean mobility enables an accurate estimation of Young's modulus and the mass density of flat panels. A numerical and an experimental study show that the method is robust, and that it requires solely a few measurement points.