Experimental Identification of Nonlinearities under Free and Forced Vibration using the Hilbert Transform

Abstract

In this paper we discuss the experimental identification of a nonlinear vibrating mechanical system. The system under test incorporated several spring and damping related nonlinearities. Indeed, in this paper we use data from a real laboratory device thus increasing the confidence in the proposed methods that have been previously applied mostly to simulated data. A unique feature of the identified model is that it shows the dependency of the estimated parameters on the vibration amplitude. The provided measurements of free and forced vibration motion, together with the unique signal processing, based on the Hilbert transform analysis, yield an accurate estimation of nonlinear spring and friction parameters of the vibration model. The obtained natural frequencies and friction parameters are functions rather than scalars that describe the system’s behavior under different operating conditions. This paper complements previously published Hilbert transform analytical methods with experimental and numerical results.