Identification and Parameter Estimation of Nonlinear Damping Using Volterra Series and Multi-Tone Harmonic Excitation

Purpose Response characteristics of nonlinear systems have been extensively studied for system identification. But all these studies mainly employ single tone harmonic excitation. In contrast, there are very few research literatures on the use of multi-tone harmonic excitation, obviously due to the challenges in more complicated formulation of response characteristics. This research intends to identify a polynomial type of damping nonlinearity using Higher-order Frequency Response Functions (HoFRFs) and harmonic amplitude measurement data under multi-tone harmonic excitation. Methods In the present study, the Volterra series is employed to demonstrate benefits of using multi- tone harmonic excitation for identification of damping nonlinearity. It is shown a large number of combination tones of higher harmonics are formed in the response spectrum. Response harmonic amplitude series are formulated for these harmonics using higher order Volterra kernel synthesis for both symmetric and asymmetric forms of damping nonlinearity. Results and conclusion A novel parameter estimation algorithm is presented to first estimate the nonlinear parameter and then the linear modal parameters of the system using two experiments only, whereas, for single-tone harmonic excitation, one would require at least six to eight experiments. The signal strength of higher harmonics is studied for selection of most effective frequency combinations in the multi-tone excitation. Numerical simulations with a typical two-tone excitation demonstrate that fairly accurate estimates of nonlinear damping parameters and linear modal parameters can be obtained with proper selection of frequency pair and excitation level.