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.

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