Complex dynamic stiffness identification of panels using inverse methods based on optical deflectometry measurements

The Virtual Fields Method and the Force Analysis Technique are two inverse methods that can be applied to identify the bending stiffness normalised by mass per unit area and the loss factor of a Love–Kirchhoff plate. To be applied, both methods require a measured displacement field. This can be measured using optical deflectometry, a full-field measurement technique. However, in optical deflectometry, it is the first-order spatial derivatives of the displacement (also known as slope fields) that are measured and not the displacement directly. This paper proposes new formalisms for the Virtual Fields Method and the Force Analysis Technique so that the methods can be applied using only the slope fields. This process of coupling the two inverse methods with optical deflectometry also involves accurately estimating the spatial step of the experimental mesh. A procedure for measuring this quantity accurately is proposed in this article. The new formalisms are tested and validated with numerical and experimental data, which are used to estimate the bending stiffness normalised by the mass per unit area and the loss factor of a Love–Kirchhoff plate.