任意边界条件下板壳类周期结构声子带隙特性研究

Plate and shell structures are widely encountered in the marine and other engineering fields, the investigating on the dynamic design and vibration control for this kind structures will be of universal significance in both theory and practice. Based on the theory of phononic crystals, the traditional structures can be designed to the periodic structural forms, such that the vibration and noise of structural system may be controlled in the source of structural design. The phenomenon of vibration band gaps exhibited in periodic structure provides a new approach for the design and vibration control of plate and shell structures. However, there is very little effort made on the related study for periodic plate and shell structures, and the current study is limited by complex boundary conditions in practice. In this project, a multiplex improved Fourier series approach will be employed to establish the prediction model for the vibration analysis of periodic plate and shell structures with general boundary conditions, and the Bragg scattering and locally resonant gap mechanisms can be investigated by applying the theory of phononic crystals. Based on the developed model, the influences of boundary conditions, structural and material parameters of phononic crystals on the energy band structure and transmission path will be deeply discussed and revealed. It is believed that the conduction of this project will provide new insight and model basis for the further dynamic design and vibration control of such periodic structures.

板壳类结构是一类在舰船及其它工程领域中常见的结构形式，开展此类结构的动力学设计以及振动噪声控制研究具有重要而普遍的意义。应用声子晶体理论可实现在结构设计的源头抑制振动噪声，将结构设计为周期性的结构形式，使之具有振动带隙特性，这为板壳类结构设计及其振动噪声控制提供了新的思路。然而，现有对于板壳类周期结构的声子带隙研究还远远不够，并且受困于边界条件的限制。本课题旨在采用一种复合的改进傅立叶级数方法，建立任意边界条件下板壳类周期结构振动的解析模型，基于声子晶体理论深入研究板壳类布拉格散射型和局域共振型周期结构声子带隙特性。在此基础上，探讨边界条件、声子结构及材料参数对于板壳类周期结构振动的能带结构与传输特性影响，深刻揭示板壳类周期结构的振动带隙机理以及边界条件影响振动带隙特性的物理机制。通过本课题的研究，为人们继续开展此类周期结构的动力学设计及其振动噪声控制提供全新的认识和通用性的分析模型基础。

应用声子晶体理论可实现在结构设计的源头抑制振动噪声，将结构设计为周期性的结构形式，使之具有振动带隙特性，这为板壳类结构设计及其振动噪声控制提供了新的思路。本课题采用一种复合的改进傅立叶级数方法，建立任意边界条件下板壳类周期结构振动的解析模型，只需改变模型中的边界约束刚度系数、几何位置函数即可得到不同材料属性、不同几何位置以及不同边界条件下的布拉格散射型以及局域共振型声子晶体动力学模型。进而，基于声子晶体理论深入研究了板壳类布拉格散射型和局域共振型周期结构声子带隙特性。在此基础上，探讨了边界条件、声子结构及材料参数对于板壳类周期结构振动的能带结构与传输特性影响。通过本项目的研究，为人们继续开展此类周期结构的动力学设计及其振动噪声控制提供全新的认识和方法参考，相关研究成果可应用于舰船结构系统的振动噪声控制，为提升舰船声隐身性能提供技术支撑。