Flexural wave bandgap properties of phononic crystal beams with interval parameters

Abstract

Uncertainties are unavoidable in practical engineering, and phononic crystals are no exception. In this paper, the uncertainties are treated as the interval parameters, and an interval phononic crystal beam model is established. A perturbation-based interval finite element method (P-IFEM) and an affine-based interval finite element method (A-IFEM) are proposed to study the dynamic response of this interval phononic crystal beam, based on which an interval vibration transmission analysis can be easily implemented and the safe bandgap can be defined. Finally, two numerical examples are investigated to demonstrate the effectiveness and accuracy of the P-IFEM and A-IFEM. Results show that the safe bandgap range may even decrease by 10% compared with the deterministic bandgap without considering the uncertainties.