Investigating the Influence of Mechanical Property Variability on Dispersion Diagrams Using Bayesian Inference

Phononic crystals are periodic structures that exhibit frequency ranges where elastic waves cannot propagate, also known as Bragg scattering band gaps. This study aims at simulating dynamic response of a periodic plane frame structure using Bayesian statistics to understand the bandgap behavior with respect to the variability in the Young’s modulus and mass density. The spectral element method is used to compute Frequency Response Functions (FRF). The spatial distribution of simulated FRFs at each frequency is used as a virtual measurement, from which the wavenumbers are obtained via a Prony type method. A Markov chain Monte Carlo (MCMC) algorithm which considers the difference between the simulated and virtually observed wavenumbers is used to simulate the posterior distribution of the mechanical properties. Stochastic dispersion diagrams are simulated via Monte Carlo from these posterior distributions. The MCMC algorithm, by using the additional information related to the wavenumber, presented a more precise wavenumber dispersion estimation. These investigations are relevant due to the expected variability of mechanical properties of periodic frame structures made by additive manufacturing.