Characterization and identification of damping and nonlinear systems parameters with bispectral analysis

A. H. Nayfeh, M. R. Hajj, J. Fung, S. O. Fahey

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We propose a consistent methodology whereby perturbation techniques, complex Fourier amplitudes, and higher-order statistics can be combined to characterize and quantify the damping and parameters of nonlinear systems. The methodology is used to characterize and quantify the damping and parameters of the first mode of a three-beam two-mass frame. The frame is excited harmonically near twice the natural frequency of its first mode. The generalized coordinate of this mode is modeled with a second-order nonlinear equation with quadratic and cubic geometric nonlinearities, a cubic inertia nonlinearity, linear and quadratic damping, and parametric and external excitation terms. The method of multiple scales is used to obtain a second-order approximate solution of this equation. This solution shows how the response amplitude and frequency content and phase difference between that of the excitation and response depend on the damping, nonlinear system parameters, and excitation amplitude and frequency. Measurements of the response amplitude, "phase difference" obtained from the bispectrum, and complex Fourier amplitudes at the excitation frequency and its one-half, under different excitation levels are then used to determine the damping and nonlinear parameters.

Original languageEnglish
Title of host publication16th Biennial Conference on Mechanical Vibration and Noise
ISBN (Electronic)9780791880425
DOIs
StatePublished - 1997
EventASME 1997 Design Engineering Technical Conferences, DETC 1997 - Sacramento, United States
Duration: 14 Sep 199717 Sep 1997

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume1C-1997

Conference

ConferenceASME 1997 Design Engineering Technical Conferences, DETC 1997
Country/TerritoryUnited States
CitySacramento
Period14/09/9717/09/97

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