Nonparametric identification of asymmetric nonlinear vibration systems with the Hilbert transform

• Published in: Journal of sound and vibration Vol. 331; no. 14; pp. 3386 - 3396
• Main Author: Feldman, M.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 02.07.2012; Elsevier
• Subjects: Asymmetry; Duffing oscillators; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mathematical models; Nonlinearity; Physics; Solid mechanics; Sound; Structural and continuum mechanics; Transforms; Vibration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Non linear oscillator; Vibration; Asymmetry; Double well model; Information system; Non linear model; Non parametric estimation; Duffing equation; Non linear effect; Hilbert transformation
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2012.02.025

The objective of the paper is presenting a simple and more accurate technique for precise identification of nonlinear elastic force functions acting in asymmetric vibration systems. The identification procedure based on the Hilbert transform is a nonparametric one; it does not require a priori information about the system structure or its parameters. The examples of the identification of asymmetric classic vibration nonlinear models – the Helmholtz and the double-well Duffing oscillators – are investigated. ► The Hilbert transform decomposes a solution into harmonics and aperiodic components. ► Their combination forms a congruent envelope and an instantaneous frequency. ► The congruent functions present two skeleton curves of an asymmetric system solution. ► They also build precisely initial nonlinear elastic force characteristics. ► Two models are investigated: the Helmholtz and the Duffing–Holmes oscillators.