Damping for large-amplitude vibrations of plates and curved panels, part 2: Identification and comparisons

A non-linear identification technique based on the harmonic balance method is presented to obtain the damping ratio and non-linear parameters of isotropic and laminated sandwich rectangular plates and curved panels, subjected to harmonic excitation orthogonal to the surface. The response of structures under consideration is approximated by a single-degree of freedom Duffing oscillator accounting for viscous damping, quadratic and cubic non-linear stiffness. The method uses experimental frequency-amplitude data and a least-squares technique to identify parameters and reconstruct frequency-response curves by spanning the excitation frequency in the neighborhood of the lowest natural frequencies. In particular, an iterative procedure is implemented to construct the mean displacement and identify the damping ratio. Close agreement is seen between the reconstructed non-linear frequency-amplitude curves, the experimental data and the results of the reduced-order model obtained in part 1 of the present study (Alijani et al., 2015 [1]). The proposed identification technique confirms the very large increase of damping during large-amplitude vibrations, as observed in part 1 of the present study, and demonstrates a non-linear correlation between damping, vibration amplitude and excitation level.