A Time Domain Procedure for the Identification of Periodic Structures

A procedure for the identification of dispersion curves and relevant mechanical characteristics of linear and nonlinear one-dimensional periodic systems is proposed herein. The procedure exploits the application of Floquet–Bloch (F–B) boundary conditions to a reference subsystem (RS) extracted from a periodic structure. The dispersion curves frequency vs. wavenumbers) are estimated from the computation of the frequency response functions (FRFs) of the subsystem for different wavenumbers in input. The proposed procedure is applied and validated on various models, including a one-dimensional locally resonant chain equipped with 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 continuous bi-material Euler–Bernoulli beam. The proposed method is particularly suitable for the experimental characterization of periodic metastructures because it exploits one single cell measurement due to two inputs to identify FRF–based dispersion curves.