A novel method to study the phononic crystals with fluid–structure interaction and hybrid uncertainty

Traditional finite element methods for the computation of the response of phononic crystals (PCs) with fluid-structure interaction (FSI) generally suffer from the dispersion error in the simulation, and the unavoidable uncertainties due to the manufactural errors and the material properties deviation. Therefore, it is important to develop an efficient numerical method to quantify the physical response of PCs with FSI. This paper presents a novel hybrid uncertain mass-redistributed finite element method (HUMR-FEM) to determine the uncertainty response of PCs with FSI. In this method, the MR-FEM is used to handle the FSI in PCs, which can minimize the dispersion error. The uncertainty of PCs is treated as random uncertainty with bounded distribution parameter instead of the precise values, and the response uncertainties are transformed into the deterministic computations of the extreme bounds of the statistical characteristics. Influences of the hybrid uncertainty on the physical responses in the design of PCs with FSI are discussed, and the accuracy and efficiency of the proposed method are validated through several numerical examples.