含区间参数的结构-声耦合系统摄动分析方法

Perturbation methods for structural-acoustic coupled systems with interval parameters

针对实际工程中普遍存在的结构-声耦合系统,充分考虑系统本身及外载荷不确定性,基于摄动理论建立一阶及高阶参数摄动两种区间分析方法。从耦合系统有限元平衡方程出发,引入区间变量对系统不确定参数进行定量化描述。据传统的一阶Taylor展式及摄动理论,可快速估算系统响应区间上下界。高阶区间参数摄动分析方法除采用改进的Taylor展式对区间矩阵、向量近似估算外,亦保留Neumann级数中部分高阶项,可有效提高响应范围的计算精度。以长方体密闭舱室为研究对象,将计算结果与传统蒙特卡洛方法对比,充分验证所提数值计算方法求解含区间参数结构-声耦合问题的可行性、有效性。

Based on the perturbation theory, two interval analysis methods named first-order interval parameter perturbation method （FIPPM） and high-order interval parameter perturbation method （HIPPM） were proposed for the structural-acoustic coupled system response prediction with interval uncertainties in both system parameters and external loads. The structural-acoustic discrete equilibrium equations were established based on the finite element method. Interval variables were used to quantitatively describe the uncertain parameters with limited information. According to the first- order Taylor series and the first-order perturbation theory, the system response interval could be quickly estimated with FIPPM. HIPPM introduced the modified Taylor series to approximately estimate the non-linear interval matrix and vector. Part of higher order terms of Neumann expansion were retained to calculate the interval matrix inverse. A 3 D cuboid model was taken as a study object, its computing results using the propose methods were compared with those using the traditional Monte Carlo method. It was shown that the proposed methods are feasible and effective to predit the sound pressure ranges of structural-acoustic coupled systems.