On the indeterminacy of orthotropic material identification through natural frequencies

This article aims to address open questions in inverse problems where natural frequencies are used to characterize unknown anisotropic materials. The analysis presented illustrates both how the characterization of the material of a thin plate, through the use of natural frequencies, can suffer from an intrinsic indeterminacy and how this indeterminacy can be challenged by using unconventional geometries of the plate itself. Such unconventional geometries are analyzed to formulate inverse problems aimed at finding a unique material characterization of plates. However, these geometries demand specific analytical approaches, such as the adoption of unconventional functional bases like two-dimensional global piecewise-smooth functions (2D-GPSFs). The use of 2D-GPSFs, in analyzing the dynamics of the mentioned 2D-geometries, even constitutes an added value; in this respect, the efficiency of these function series is also compared to previous methods proposed for the analysis of the dynamics of vibrating plates with unconventional geometries. The analyses discussed are addressed through a numerical case study that demonstrates how the use of plates with a thin L-shaped geometry allows overcoming the indeterminacy issues; furthermore, it also shown how geometric complications can be implemented by employing 2D-GPSFs as a functional basis, thus extending the possibility to identify the properties of planar specimens of different geometries.