In this paper, a single-degree-of-freedom dynamic model is described, with displacement- and 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.

在本文中，描述了一个单自由度动力学模型，其中位移和速度相关的非线性由幂定律表示。该模型旨在支持经受谐波激励的结构部件的动态识别。与其他分析表达式相比，非线性指数的数据驱动估计提供了很大的通用性，使通用模型适用于刚度和阻尼方面的多种不同非线性。例如，提出的阻尼配方可以自然地适应空气阻力（二次）阻尼以及干摩擦。与纯粹的数据驱动方法（例如黑匣子）不同，所获得的模型是完全可检查的。本文提出的公式适用于原型高柔性机翼的大振动，并适合其在频域中的稳态响应。众所周知，这些大振幅的襟翼方向弯曲振荡会受到刚度（非线性硬化）和与速度有关的阻尼项的非线性的影响。该模型针对不同的结构配置和输入幅度进行了实验验证，因为这两个非线性都取决于能量。