不确定声固耦合系统中频响应分析与优化方法研究

Uncertainties related with material properties,physical dimensions, external excitations and surrounding environments widely exist in the acoustic-structural coupled system. The mid-frequency response of the acoustic-structural coupled system is very sensitive to these uncertainties. Without considering these uncertainties, the response and optimization of the acoustic-structural coupled system yielded by deterministic numerical methods may be unreliable. In this project, we will make systematical researches on the mid-frequency response analysis of the uncertain acoustic-structural coupled system under the random model, the interval model, the hybrid random and interval model and the evidence model. The corresponding effective and efficient nondeterministic numerical methods based on the above four uncertain models will be developed. These nondeterministic numerical methods will establish the theoretical basis of the mid-frequency response analysis of the uncertain acoustic-structural coupled system. Then, comparisons among the above four uncertain models for the mid-frequency response analysis of the uncertain acoustic-structural coupled system will be presented. According to the compared results, different effects of the above uncertain models on the mid-frequency response of the uncertain acoustic-structural coupled system will be exhibited. Finally, the evidence model will be introduced into the acoustic-structural coupled system, and based on it a evidence reliability-based design optimization method will be proposed. This optimization method will provide a technology support for the optimized design of the acoustic-structural coupled system. The research works of this project will provide effective technologies for the mid-frequency response analysis and optimization of the uncertain acoustic-structural coupled system. Thus, this project has important theoretical significances and practical applications.

声固耦合系统广泛存在与材料属性、几何尺寸、外部激励和周边环境等因素相关的不确定性，其中频响应对这些不确定性因素非常敏感。忽略这些不确定性因素，采用确定性数值方法对声固耦合系统的中频响应进行分析与优化，所得结果可能存在很大误差。本项目拟基于随机模型、区间模型、随机与区间混合模型和证据理论模型，对不确定声固耦合系统的中频响应数值分析方法进行系统研究，提出相应的高效高精度不确定数值分析方法，为不确定声固耦合系统的中频响应分析提供有效途径；在此基础上对比研究各类不确定模型应用于声固耦合系统中频响应分析的特点，揭示各类不确定参数对声固耦合系统中频响应的影响规律；最后将证据理论模型引入不确定声固耦合系统，提出基于证据理论的不确定声固耦合系统优化设计方法，为不确定声固耦合系统的优化设计提供技术支撑。本项目研究工作将为不确定声固耦合系统的中频响应分析与优化提供有效的技术手段，具有重要的理论意义与应用价值。

不确定性广泛存在于各种声固耦合系统中。这对声固耦合系统的中频响应和优化有着不可忽视的影响。为得到准确的中频响应和优化结果，声固耦合系统必须考虑不确定性的影响。本项目完成了不确定声固耦合系统中频响应分析与优化方法研究，在《Computer Methods in Applied Mechanics and Engineering》、《Mechanical Systems and Signal Processing》、《Journal of Sound and Vibration》等国外重要学术期刊发表论文20余篇；培养博士生3名，硕士生5名。主要研究工作包括：（1）区间声固耦合系统中频响应分析方法研究。（2）基于证据理论的不确定声固耦合系统中频响应分析方法研究。（3）多凸集与p-box不确定声固耦合系统中频响应分析方法研究。（4）混合不确定声固耦合系统中频响应分析方法研究。（5）不确定声固耦合系统优化方法研究。上述研究工作为不确定声固耦合系统的中频响应分析与优化提供了有效的技术手段，具有重要的理论意义与应用价值。