Damping identification using perturbation techniques and higher-order spectra

Perturbation techniques and spectral moments are combined to characterize a nd quantify the damping and nonlinear parameters of the first mode of a thr ee-beam two-mass frame. The frame is excited harmonically near twice its lo west natural frequency. The response is modeled with a second-order nonline ar equation with quadratic and cubic terms and linear and quadratic damping terms. The method of multiple scales is used to obtain a second-order appr oximate solution for this model. Bispectral analysis is used to quantify th e level of coupling between modes and measure their phase difference. The a mplitudes and phase difference between the excitation and response mode wit h different frequencies are substituted into the approximate solution to de termine the damping and nonlinear parameters.