Dynamic systems, such as vibration isolators, rotor-bearing systems, are inherently nonlinear and their dynamic behaviour often cannot be sufficiently explained or predicted by simple linear models. Presence of nonlinearity leads to certain characteristic behaviours in the response such as jump phenomenon, limit cycle, super-harmonic resonances and such behaviours can be accurately predicted only if the nonlinearity structure and related parameters are properly known. This emphasises the recently growing importance of nonlinear system identification. A majority of the identification works is based on a-priori knowledge of nonlinearity structure and most of them consider only stiffness nonlinearities, such as Duffing’s oscillator and bilinear oscillator. Not much work has been reported on nonlinearity structure identification for systems with damping nonlinearities. This paper, first discusses a systematic classification of nonlinearity structures based on first, second and third harmonic response amplitudes under harmonic excitation. Characteristics response for individual nonlinearity class is explained by Volterra series response formulation with higher order Frequency Response Functions. In the second part, a typical cubic damping nonlinearity is identified from cubic stiffness nonlinearity and an algorithm for estimating the nonlinear and linear damping parameters is developed. A new term called measurability ratio is introduced to show how it can help in deciding the most appropriate excitation frequency. Effect of truncating the Volterra series response on parameter estimation error is also studied for different excitation frequencies and varying excitation levels. It is shown that, with recursive iteration in computation of third harmonic amplitude, estimation accuracy can be further improved.

诸如振动隔离器，转子轴承系统之类的动态系统本质上是非线性的，其动态行为通常无法通过简单的线性模型充分解释或预测。非线性的存在会导致响应中某些特定的行为，例如跳跃现象，极限环，超谐波共振，只有正确了解非线性结构和相关参数，才能准确预测此类行为。这强调了非线性系统识别的最新重要性。大多数识别工作基于对非线性结构的先验知识，并且大多数仅考虑刚度非线性，例如Duffing振荡器和双线性振荡器。关于具有阻尼非线性的系统的非线性结构识别的报道还很少。本文首先讨论了在谐波激励下基于一次，二次和三次谐波响应幅度的非线性结构的系统分类。具有高阶频率响应函数的Volterra级数响应公式解释了单个非线性类的特征响应。在第二部分中，从三次刚度非线性中识别出典型的三次阻尼非线性，并开发了估算非线性和线性阻尼参数的算法。引入了一个称为可测量比的新术语，以显示它如何帮助确定最合适的激励频率。对于不同的激励频率和变化的激励水平，也研究了截断Volterra级数响应对参数估计误差的影响。结果表明，通过三次谐波幅度的递归迭代，可以进一步提高估计精度。