Geometrically exact plate models for system identification via Higher-Order Spectra extracted from nonlinear dynamic responses

Plates are widely used in a broad range of engineering applications and particularly as building elements for aeronautical, mechanical, marine, and civil structures. In the great majority of applications, thin linearly elastic plate-like structures with isotropic properties are used. In the last decades, structures with orthotropic or anisotropic properties, such as composite laminated multilayered plates, are becoming widely accepted. Due to their out-of-plane flexibility, these structures might be prone to large rotations, displacements and strains, as it usually occurs in the post-buckling regime or when they are excited near resonance. In these cases, consistent mechanical models capable of capturing their static and dynamic nonlinear behaviors are needed [1-3]. However, the use of truncated nonlinear models – such as the widely used Föppl-von Kármán model which considers the stretching of the mid-plane as the dominant nonlinearity but neglects the nonlinear curvatures, shear deformations, and rotary inertia – may turn out to be inaccurate. The exemplary cases are when one aims at a careful nonlinear system identification for damage detection or at a vibration control problem. In this work, we propose a geometrically exact model capable of describing thin isotropic, orthotropic, or laminated multilayered plates. First, we show, by means of experiments (see, e.g., Fig. 1), that the equilibrium response under a quasi-static monotonically increasing point load is predicted with greater accuracy by the proposed theory compared to the Föppl-von Kármán theory. Then, with the purpose of characterizing the nonlinear behavior of the plate, we study the nonlinear dynamic properties of the responses under resonant as well as single- and multi-tone excitations, employing a Higher-Order Spectral analysis [4]. We show that the prediction of the nonlinearities in the dynamic response agrees well with our experimental results. These results pave the way to the implementation of a nonlinear system identification technique based on Higher-Order Spectra of the response obtained through the geometrically exact equations of motion.