Predicting robust complete and full band gaps in three-dimensional frame structures



Vibration can cause structural damage in dynamic systems when not designed properly. Recently, several approaches are emerging in structural dynamics as possible alternatives for passive vibration and noise control, such as phononic crystals and metamaterials. In this work, a three-dimensional frame that presents intersection of longitudinal, flexural and torsional band gaps is investigated. For periodic structures, the Irreducible Brillion Zone (IBZ) gives information for any possible angle of propagation of a wave. The manufacturing process induces variability along each three-dimensional frame element. The present study verifies the robustness of the band gaps of the three-dimensional structure against spatially varying geometry and mechanical properties. The spatial random fields are modeled using the expansion optimal linear estimator (EOLE). Bayesian statistics is used to infer on the stochastic response simulated using the Monte Carlo method combined with the EOLE. The three-dimensional frame is modeled via Euler-Bernoulli beam and ordinary shaft theories as well as  with Timoshenko and Saint-Venant theories. It is shown that the three-dimensional frame structure exhibits a complete (for all waves) and full (throughout the IBZ) robust band gap against the proposed variability. Both models are able to predict this robust band gap.