CHARACTERIZATION AND IDENTIFICATION OF DAMPING AND NONLINEAR SYSTEMS PARAMETERS WITH BISPECTRAL ANALYSIS

摘要

We propose a consistent methodology whereby perturbationtechniques, complex Fourier amplitudes, and higher-order statis-tics can be combined to characterize and quantify the damp-ing and parameters of nonlinear systems. The methodology isused to characterize and quantify the damping and parametersof the rst mode of a three-beam two-mass frame. The frameis excited harmonically near twice the natural frequency of itsrst mode. The generalized coordinate of this mode is modeledwith a second-order nonlinear equation with quadratic and cu-bic geometric nonlinearities, a cubic inertia nonlinearity, linearand quadratic damping, and parametric and external excitationterms. The method of multiple scales is used to obtain a second-order approximate solution of this equation. This solution showshow the response amplitude and frequency content and phase dif-ference between that of the excitation and response depend onthe damping, nonlinear system parameters, and excitation am-plitude and frequency. Measurements of the response amplitude,phase dierence' obtained from the bispectrum, and complexFourier amplitudes at the excitation frequency and its one-half,under dierent excitation levels are then used to determine thedamping and nonlinear parameters.