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