A generalised power-law formulation for the modelling of damping and stiffness nonlinearities

In this paper, a single-degree-of-freedom dynamic model is described, with displacementand velocity-dependent nonlinearities represented by power laws. The model is intended to support the dynamic identification of structural components subjected to harmonic excitation. In comparison to other analytical expressions, the data-driven estimation of the nonlinear exponents provides a large versatility, making the generalised model adaptable for a wide number of different nonlinearities in both stiffness and damping. For instance, the proposed damping formulation can naturally accommodate air drag (quadratic) damping as well as dry friction. Differently to purely data-driven methods (e.g. black boxes), the obtained model is fully inspectable. The proposed formulation is here applied to the large oscillations of a prototype highly flexible wing and fitted on its steady state response in the frequency domain. These large-amplitude flap-wise bending oscillations are known to be affected by nonlinearities in both the stiffness (nonlinear hardening) and the velocity-dependent damping terms. The model is validated against experiments for different structural configurations and input amplitudes, as both these nonlinearities are energy-dependent.