Multi-output subspace identification of complex Bloch wavenumbers in 1D periodic structures

The experimental characterization of complex dispersion curves is challenging in phononic crystals, composites, periodic, architected or metamaterials. Recent studies have highlighted the importance of subspace identification methods in determining wave propagation properties through complex wavenumbers and, consequently, in characterizing a complex structure experimentally. Still, such methods have not yet been adapted for 1D periodic structures with periodic sampling limitations. This work introduces a Subspace-based complex Bloch WAveNumber identification method (SWAN) which can take advantage of full-field vibration measurements (i.e., multiple data points per unit cell) to statistically reduce the negative impact of having a limited number of unit cells. The SWAN method is based on a state-space representation of the wave finite element method. A symplectic state-space model is formulated and mathematically proved to represent the original system. Eventually, the proposed method enhances complex wavenumber estimates when a small number of unit cells is available. In addition, a general-purpose, adaptive spectral mask is introduced to reject physically irrelevant identification results, enabling straightforward denoising of the identified dispersion curves. The proposed approach is validated through numerical and experimental applications. • Subspace-based identification of complex wavenumbers in 1D periodic structures. • Multi-modal & multi-output wavenumber identification. • State-space model proposed for symplectic subspace identification. • Enhanced bandgap characterization with full-field vibration measurements. • General-purpose spectral mask for wavenumber selection.