Damping identification using perturbation techniques and higher-order spectra

Perturbation techniques and spectral moments are combined to characterize and quantify the damping and nonlinear parameters of the first mode of a three-beam two-mass frame. The frame is excited harmonically near twice its lowest natural frequency. The response is modeled with a second-order nonlinear equation with quadratic and cubic terms and linear and quadratic damping terms. The method of multiple scales is used to obtain a second-order approximate solution for this model. Bispectral analysis is used to quantify the level of coupling between modes and measure their phase difference. The amplitudes and phase difference between the excitation and response mode with different frequencies are substituted into the approximate solution to determine the damping and nonlinear parameters.