A time domain procedure for the identification of periodic structures

A procedure for the identification of dispersion curves and mechanical characteristics of linear and nonlinear one-dimensional (1D) periodic structures is proposed herein. The procedure exploits the application of Floquet– Bloch (F–B) boundary conditions to a reference subsystem (RS) extracted from a mechanical metastructure. The dispersion curves (frequency vs. wavenumbers) are estimated from the computation of the frequency response functions (FRFs) of the RS for different wavenumbers in input. The proposed procedure is applied and validated on various models, including a 1D mass-in-mass system characterized by cubic nonlinear springs. As expected, the nonlinear system exhibits a distinct dependence on the amplitude of the excitation. In addition, a revised application of the subspace identification (SI) method is exploited for the identification of hardening-type nonlinear mechanical characteristics. For the sake of completeness, the identification procedure is also tested on a waveguide in axial and flexural vibrations. Due to its single output from a measuring cell, and two inputs, the proposed method is particularly suitable for the experimental characterization of periodic structures.