Modified sub-interval perturbation finite element method for 2D acoustic field prediction with large uncertain-but-bounded parameters

Based on the sub-interval perturbation analysis, a modified sub-interval perturbation finite element method is proposed to determine the bounds of sound pressure in the 2D acoustic field with large uncertain-but-bounded parameters. In the proposed method, the inversion of the invertible sub-interval dynamic stiffness matrix is approximated by a modified approximate interval-value Sherman–Morrison–Woodbury formula to overcome the drawbacks arising from the dependency phenomenon of parameters and the unpredictable effect of neglecting the higher order terms in Neumann series. The modified sub-interval perturbation procedures are implemented in a numerical finite element framework. Numerical results on a 2D acoustic tube and a 2D acoustic cavity of a car with large uncertain-but-bounded parameters evidence the remarkable accuracy and effectiveness of the proposed method.

► S-IFEM is proposed for 2D sound field with uncertain parameters.
► MS-IFEM is proposed for 2D sound field with uncertain parameters.
► MS-IFEM achieves higher accuracy as compared with S-IFEM.
► Increasing number of sub-intervals will increase accuracy MS-IFEM.