Finite Element Analysis of the Uncertainty of Physical Response of Acoustic Metamaterials with Interval Parameters

Abstract

The physical response of acoustic metamaterials may change due to the variation of the material properties in the manufacture process. Thus, an interval perturbation finite element method is formulated to study the mechanical response of acoustic metamaterials with the interval parameters, which includes the uncertainty effects on the band structure, resonance mode and frequency response of acoustic metamaterials. By virtue of the first-order Taylor series expansion and sensitivity analysis of dynamic properties of acoustic metamaterials with respect to the interval parameters, the interval perturbation finite element method established in this work can predict the upper and lower bounds of the dynamic properties of the acoustic metamaterials. Three numerical examples are studied to validate the effectiveness of the interval perturbation finite element method to analyze the physical response of acoustic metamaterials with the interval parameters, and the results calculated by Monte Carlo method are regarded as the reference results to validate the interval perturbation finite element method. The uncertainty model constructed by interval perturbation finite element method provides a great help in the design of acoustic metamaterials.