Most of the dynamic systems are inherently nonlinear either with stiffness nonlinearity or with damping nonlinearity. Presence of nonlinearity often leads to characteristic behaviours in response such as jump phenomenon, limit cycle and super-harmonic resonances. Such behviours can be accurately predicted only if the nonlinearity structure and related parameters are properly known. A majority of identification works is based on a-priori knowledge of nonlinearity structure and most of them consider only stiffness nonlinearities. Not much work has been reported on identification and parameter estimation in the area of damping nonlinearities. This paper presents a systematic classification of asymmetric damping nonlinearity and develops a parameter estimation algorithm using harmonic excitation and response amplitudes in terms of higher order Frequency Response Functions. The asymmetry in damping nonlinearity is modeled as a polynomial function containing square and cubic nonlinear terms and then Volterra series is employed to derive the response amplitude formulation for different harmonics using synthesied higher order Frequency Response Functions. Detailed numerical study is carried out with different combinations of square and cubic nonlinearity parameters to investigate appropriate excitation level and frequency so as to get measurable signal strength of second and third harmonics and at the same time keeping the Volterra series approximation error low. The estimation algorithm is first presented for nonlinear parameters and then it is extended for estimation of linear parameters including damping ratio. It is demonstrated through numerical simulation that nonlinear damping parameters can be accurately estimated with proper selection of excitation level and frequency.

大多数动力学系统固有地是非线性的，具有刚性非线性或阻尼非线性。非线性的存在通常导致响应中的特征行为，例如跳跃现象，极限环和超谐波共振。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。大多数识别工作是基于对非线性结构的先验知识，并且大多数都仅考虑刚度非线性。在阻尼非线性方面，关于识别和参数估计的工作还很少。本文介绍了非对称阻尼非线性的系统分类，并根据高阶频率响应函数，开发了一种使用谐波激励和响应幅度的参数估计算法。将阻尼非线性的不对称性建模为包含平方和三次非线性项的多项式函数，然后使用Volterra级数使用合成的高阶频率响应函数来导出不同谐波的响应幅度公式。对不同的平方和三次非线性参数组合进行了详细的数值研究，以研究合适的激励电平和频率，从而获得可测量的二次谐波和三次谐波的信号强度，同时保持Volterra级数的逼近误差较低。首先提出了针对非线性参数的估计算法，然后将其扩展为包括阻尼比在内的线性参数的估计。它是通过数值模拟表明，非线性阻尼参数可以与激发水平和频率的适当选择来精确地估计。