Band Gap Properties in Metamaterial Beam with Spatially Varying Interval Uncertainties

First, this study proposed a metamaterial beam model with spatially varying interval density. The dynamic equation of could be established by incorporating the decomposition results field based on Karhunen–Loeve expansion into finite element method. An perturbation method was developed to evaluate bounds response vector. Then, an vibration transmission analysis performed, and frequency range safe band gap determined. Meanwhile, Monte Carlo simulations vertex are also presented provide reference solutions. By comparison, it found that calculation accuracy acceptable. numerical showed significantly smaller than deterministic gap.