Identification and parameter estimation of non-polynomial forms of damping nonlinearity in dynamic systems

Abstract

Damping is often assumed to viscous and linear in modelling a dynamic system. However, damping is inherently nonlinear and often is in non-polynomial forms such as Coulomb damping, bilinear, or quadratic damping. Recently, non-polynomial forms of damping have found wide applications in vibration isolators and absorbers. However, not much study is available for the identification of these non-polynomial forms of damping. The present work attempts to develop an identification and parameter estimation procedure for two non-polynomial damping forms, i.e., bilinear damping and quadratic damping. First, response harmonic amplitudes are formulating using Volterra series and equivalent linearised damping; and then they are compared with representative polynomial forms, i.e., square damping and cubic damping. Bilinear damping was identified employing a method of harmonic probing and studying first and second harmonic amplitude characteristics. Similar way, quadratic damping is identifying using first and third harmonic characteristics. Finally, a parameter estimation procedure is developed as a step-by-step algorithm and demonstrated through numerical simulation and error analysis. It is shown that reasonable accuracy can be obtained in estimation of the nonlinear parameters with proper selection of excitation frequencies and excitation levels.