不确定声场分析的二阶区间摄动有限元法

针对一阶区间摄动有限元法在声场参数不确定程度增大时误差过大的缺陷,在二阶Taylor展开的基础上推导了声学二阶区间摄动有限元法,并将其应用于区间不确定声场的声压响应分析。该方法先对声学区间有限元方程的声压响应向量进行二阶Taylor展开,获取声压响应的二阶近似响应向量;再根据二次函数极值定理获得声压响应向量的上下界。二维管道声场与轿车声腔模型的数值分析算例表明,与一阶区间摄动有限元法相比,二阶区间摄动有限元法有效提高了计算精度。因此二阶区间摄动有限元适合不确定度更大的区间不确定声场声压响应分析,具有良好的工程应用前景。

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.