敷设复杂声学覆盖层的板壳结构声振特性的理论建模及仿真分析

The multi-layer plate and shell structures typically treated with the sub-layers consisting of a homogeneous viscoelastic layer, a viscoelastic layer with cavities, a porous absorbing material layer, are representative structures among the modern acoustic coating. They have superior application future in the aerospace field, transportation and transport field. However, up till now, theory analysis as well as design methods for these kinds of structures are still deficient. Hence, relevant study on this aspect is urgent, especially on the theory modeling, analysis methods and mechanism study for them. Aiming at this kind of structures, the project attempts to propose a mechanic model for analyzing the vibro-acoustic performance on them. Firstly, sub layers are divided from the whole structures. Pointing at each sub layer, a similar treatment alike the isoparametric element way used in FEM was pointed out to map the irregular shaped layer into the regular one. Subsequently. Each mapped sub-layer would be modelled respectively. Among them, plates and shells theory combined with the traditional Biot‘s theory was applied to the modelling on porous absorbing sub-layer. Moreover, effective medium method would be used for the modelling on the viscoelastic sub-layer with or without cavity. Then, combing with modern mathematical methods, a semi-analytical solving method would be developed, and corresponding experiment would be carried out to prove the validity of the mechanic model and its solving method. Based on this, the action mechanism for different parameters of the complex acoustic coating layer on the vibration and radiation performance of the plates and shells treated with different kinds of acoustic coating would be investigated, in order to provide supporting theories and technology for the design of the complex acoustic coating layer.

由均匀粘弹材料层、含空腔的粘弹材料层和多孔介质层组成的多层复杂声学板壳结构，具有阻尼、隔声、吸声等多种功能，在现有声学覆盖层中极具代表性，并在航空航天，交通运输工程中具有极佳的应用前景。但就目前来看，无论是该类结构的理论分析还是设计手段都还存在较大的缺陷，需要进一步的深入研究。本项目针对这类多层板壳结构，采用分层理论，首先将各子层进行细化，针对各子层，采用等参单元的类似处理方法，将不规则的子层等参处理为矩形单元；随后，对各子层分别建模；其中，对多孔吸声细层，将结合板壳振动理论和Biot 理论进行建模，对含空腔的粘弹性材料细层和粘弹性材料细层则将采用等效媒质法进行建模；此后，结合齐次扩容精细积分技术及配点法建立该耦合模型的求解方法，并通过实验或数值仿真实验验证其有效性。以本项目研究为基础，探索不同类型声学覆盖层参数对板壳声振特性的影响，为不同声学覆盖层的优化设计提供理论支持和和技术支撑。

含多孔介质吸声材料的多层复杂声学板壳结构，在现有声学覆盖层中极具代表性，并在航空航天，交通运输工程中具有极佳的应用前景。但就目前来看，无论是该类结构的理论分析还是设计手段都还存在较大的缺陷，需要进一步的深入研究。本项目针对这类多层板壳结构，采用分层理论，首先将结构细化成子层，采用等参思想和摄动理论，将不规则的子层等参处理为形状规则的子结构；随后，对多孔吸声细层，结合板壳振动理论和Biot理论进行建模，对含空腔的粘弹性材料细层和粘弹性材料细层则采用等效媒质法进行建模；此后，结合齐次扩容精细积分技术及配点法建立该耦合模型的求解方法，并通过实验和数值仿真实验验证其有效性。针对以上研究内容，获得了以下研究成果（1）项目采用传递矩阵法和精细元法分别建立了多孔吸声矩形薄板和圆柱壳声振特性分析的半解析模型，这些解析模型充分考虑了薄板或薄壳面内振动与弯曲振动的相互耦合，比现有的解析模型更加接近多孔板壳的真实振动。同时，采用了一种高精度的齐次扩容精细积分法进行求解，可以在中高频段保证其精确性。此外，该模型的运动控制方程的状态向量中的各物理量均具有明晰的物理意义，更利于各种边界条件的应用。（2）采用等参单元思想和摄动理论得到了不规则板壳动力学问题的一阶常微分矩阵方程，将高精度的齐次扩容精细积分法进一步拓展到形状不够规则的板壳结构中，增强了其适用性；（3）本项目实验人员采用LMS测试系统对板壳结构的声振进行了一系列的测试分析，包括商用车的声振检测中。测试结果验证了本项目建立的模型的精确性。该测试手段可为进一步拓展到后续多层声学结构的声振测试。（4）采用数值模拟手段，对含多孔吸声材料的多层声学结构的几何和物理参数对其声振性能的影响进行了探讨，并初步建立了三维多孔吸声介质的光滑有限元模型。（5）对含空腔的吸声结构的声振特性进行了初步探讨。基于以上研究，本项目可为不同声学覆盖层的优化设计提供理论支持和和技术支撑。