Second-order interval perturbation finite element method for the analysis of the acoustic filed with uncertain parameters

Abstract Aiming at the problem that the accuracy of the first-order interval perturbation method is not satisfactory when it is used for the response analysis of the acoustic filed with large uncertain levels, the acoustical second-order interval perturbation finite element method is proposed based on the second-order Taylor series expansion and the acoustic FEM method. In the acoustical second-order perturbation finite element method, the non-deterministic sound pressure vector of the acoustic filed with interval parameters is expanded to the second order Taylor series. The upper and lower bounds of the sound pressure response are evaluated latter in the inner feasible domain of the interval parameters based on the extreme value theorem. Numerical results on a 2D acoustic tube and a 2D acoustic cavity of a car with interval parameters show that the second-order interval perturbation finite element method achieves higher accuracy compared with the first-order interval perturbation finite element method. Hence, the second-order interval perturbation finite element method can be well applied in analyzing the acoustic filed with larger uncertain levels, and has a wide application foreground.