CAJ | 학술논문

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。
침대실제공정중보편존재적결구－성우합계통，충분고필계통본신급외재하불학정성，기우섭동이론건립일계급고계삼수섭동량충구간분석방법。종우합계통유한원평형방정출발，인입구간변량대계통불학정삼수진행정양화묘술。거전통적일계 Taylor 전식급섭동이론，가쾌속고산계통향응구간상하계。고계구간삼수섭동분석방법제채용개진적 Taylor 전식대구간구진、향량근사고산외，역보류 Neumann 급수중부분고계항，가유효제고향응범위적계산정도。이장방체밀폐창실위연구대상，장계산결과여전통몽특잡락방법대비，충분험증소제수치계산방법구해함구간삼수결구－성우합문제적가행성、유효성。
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.HIPPMintroduced 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 3D 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.