Bayesian statistics of uncertainty quantification attenuation bands of three-dimensional phononic lattices
Palavras-chave:
Three-dimensional wave propagation, Phononic crystal, Uncertainty quantification, Periodic structure, Vibration passive controlResumo
Phononic crystals are periodic structures that may present Bragg scattering and wave coupling band
gaps, which are frequency ranges where waves cannot propagate freely. In this work, it is proposed a three-
dimensional frame structure that can be used to support and isolate vibrations of a rigid payload. This structure is
a 3D lattice made of frame elements. Firstly, one frame presenting the intersection of longitudinal, flexural, and
torsional band gaps were proposed. The resulting unit cell is modeled via the spectral element method (SEM).
The three-dimensional structural model includes constraints and inertial characteristics of a rigid body attached
at its top. Pseudo experiments are performed using mechanical property values sampled from previously defined
statistical distributions. A Markov chain Monte Carlo (MCMC) algorithm is used to estimate posterior distributions
of mechanical properties considered as statistical variables. Prony’s method is used in the MCMC algorithm to
improve its precision. The Monte Carlo method is used to infer about the stochastic wavenumber. Two robust and
complete attenuation bands related to the considered variability are observed, which are shown on the dispersion
diagram of the 3D structure for some observations along the contours of the irreducible Brillouin zone (IBZ). Such
attenuation bands can also be observed on the forced response of the rigid payload subjected to base excitations.
