Year: 2026
Type: conference-paper
Abstract: We introduce a general framework for computing nonlinear dispersion relations in homogeneous and periodic media exhibiting smooth nonlinearities.The method relies on a multi-harmonic expansion of nonlinear Floquet-Bloch waves, resulting in a nonlinear system of equations that can be efficiently approximated using the Harmonic Balance Method.As an illustrative example, the approach is first applied to a geometrically nonlinear Euler-Bernoulli beam, from which we derive amplitude-dependent dispersion relations and corresponding waveforms.We then extend the methodology to arbitrary finite element (FE) models, thereby generalizing the Wave Finite Element Method to nonlinear regimes, before applying it to a geometrically nonlinear locally resonant metamaterial.Although computationally intensive for full FE models, the proposed framework provides a powerful tool for designing complex nonlinear metamaterials..
Source: Lirias (KU Leuven)
Authors: Boukadia, Régis, Deckers, Elke
Institution: KU Leuven
Language: English
Subfield: Acoustics and Ultrasonics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221237998