Identification and Parameter Estimation of Asymmetric Nonlinear Damping in a Single-Degree-of-Freedom System Using Volterra Series

Abstract

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.