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

Marco Civera; Stefano Grivet-Talocia; Cecilia Surace; Luca Zanotti Fragonara

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

机译：用于阻尼和刚度非线性建模的广义电力法制定

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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.

机译：在本文中，描述了一种自由度的动态模型，具有由动力法表示的位移和速度相关的非线性。该模型旨在支持经受谐波激发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大的通用性，使得广义模型适用于刚度和阻尼的各个不同的非线性。例如，所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。不同于纯粹的数据驱动方法（例如黑匣子），所获得的模型是完全检测的。该所提出的制剂在这里应用于原型高度柔性翼的大振荡，并在频域中安装在其稳态响应上。已知这些大幅度襟翼弯曲振荡刚度（非线性硬化）和速度依赖性阻尼术语中的非线性影响。根据不同结构配置和输入幅度的实验验证该模型，因为这两种非线性都是能量相关的。

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来源
《Mechanical systems and signal processing》 |2021年第5期|107531.1-107531.21|共21页
作者
Marco Civera; Stefano Grivet-Talocia; Cecilia Surace; Luca Zanotti Fragonara;
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作者单位

Department of Mechanical and Aerospace Engineering Politecnico di Torino 10129 Turin Italy;

Department of Electronics and Telecommunications Politecnico di Torino 10129 Turin Italy;

Department of Structural Building and Geotechnical Engineering Politecnico di Torino 10129 Turin Italy;

Centre for Autonomous and Cyber-Physical Systems Cranfield University Cranfield Bedford MK43 0AL UK;

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正文语种 eng
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Nonlinear dynamics; Nonlinear hardening; Nonlinear damping; Large vibrations; Nonlinear system identification; High-Aspect-Ratio wing;

机译：非线性动力学;非线性硬化;非线性阻尼;大振动;非线性系统识别;高纵横比翼;

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

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