Abstract In the identification of mechanical systems through inverse receptance methods, a linear model is usually assumed, at least on a first approximation. However, most of the systems have a degree of nonlinearity in their elastic or dissipative properties. Usually, stiffness nonlinearities are identified, while damping nonlinearities are neglected or even not detected. Indeed, an equivalent linear damping model, correctly representing the nonlinear dissipation of the system under testing condition, can always be found, but it is test-specific and not generally valid. This paper addresses the identification of dissipative models for multi degrees of freedom mechanical systems with a single damping nonlinearity. Based on the direct damping matrix identification through inverse receptance methods, this research proposes an extension of the Stabilised Layers Method, valid for linear systems, to damping nonlinearities, resulting in the identification of the test-independent linear and nonlinear damping matrices of the system. The proposed method is theoretically derived for the identification of nonlinear damping forces depending on powers of displacement and velocity. The sinusoidal input describing function approximation of the nonlinear damping is exploited to identify the coefficients of the nonlinear damping force from the system receptances, measured under sinusoidal sweeps at constant amplitudes of oscillation across the nonlinearity. The presented method is applied to identify the linear and nonlinear damping matrices of a multi degrees of freedom system with a localised nonlinear magnetic damper. The coefficients of the nonlinear magnetic damping force are identified for two configurations of the magnetic damper. The proposed approach is a parametric method to identify the nonlinear damping models of mechanical systems using standard experimental techniques usually adopted for linear systems. The identified model is valid under general excitation forces, predicting the system behaviour in a broader range of operation than the test-specific linear equivalent model.

中文翻译：

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非线性阻尼的直接识别：应用于磁阻尼系统

摘要 在通过逆接收方法识别机械系统时，通常假设线性模型，至少在一次近似上。然而，大多数系统在其弹性或耗散特性方面具有一定程度的非线性。通常，刚度非线性被识别，而阻尼非线性被忽略或什至没有被检测到。事实上，总是可以找到一个等效的线性阻尼模型，正确地表示测试条件下系统的非线性耗散，但它是特定于测试的，通常不是有效的。本文讨论了具有单阻尼非线性的多自由度机械系统的耗散模型的识别。基于逆接收法的直接阻尼矩阵识别，本研究建议将适用于线性系统的稳定层方法扩展到阻尼非线性，从而识别系统的与测试无关的线性和非线性阻尼矩阵。所提出的方法从理论上推导出用于识别依赖于位移和速度的幂的非线性阻尼力。利用描述非线性阻尼函数逼近的正弦输入来识别来自系统接收的非线性阻尼力的系数，在非线性振荡的恒定振幅下在正弦扫描下测量。所提出的方法用于识别具有局部非线性磁阻尼器的多自由度系统的线性和非线性阻尼矩阵。针对磁阻尼器的两种配置确定了非线性磁阻尼力的系数。所提出的方法是使用通常用于线性系统的标准实验技术来识别机械系统的非线性阻尼模型的参数化方法。识别的模型在一般激励力下是有效的，与测试特定的线性等效模型相比，可以在更广泛的操作范围内预测系统行为。