复杂组合结构全频域高效高精度振动分析方法研究

Complex beam, plate and shell built-up structures has been widely used in engineering structures (and components) such as high-speed trains, aircraft, ships and submarines. The dynamic characteristics play a significant role in the comfort, safety and reliability of these structures. Mid- and high-frequency vibration analysis of these structures has been a research hotspot and difficulty which still remains immature. Dynamic Stiffness method has been used successfully in the modal and dynamic response analyses due to its exactness and highly computational efficiency. However, the DSM has been seriously restricted to one-dimensional (1D) structures as well as prismatic two-dimensional (2D) structures with a pair of opposite edges simply supported. This research will focus on complex beam-plate-shell built-up structures with complex combination forms and subjected to any arbitrary boundary conditions, in order to develop highly accurate spectral dynamic stiffness (SDS) models within the full frequency range; the corresponding improved Wittrick-Williams algorithm will be developed for the modal analysis, the SDS method will be applied in conjunction with proper linear transformations for the dynamic response of structures, and those computational techniques will be optimised for higher efficiency; the developed algorithms will be used to engineering structures e.g., sandwich panels with corrugated cores, composite wing-boxes of aircraft and etc., which will be validated by numerical and experimental analysis. This research aims to provide a highly efficient, accurate and reliable program for the parametric and optimization analysis of complex built-up structures within the full frequency range; and to offer benchmark solutions and key parameters for other methods. Therefore, the research is of great theoretical significance and practical value.

复杂梁板壳组合结构被广泛运用于高速列车、航空航天、舰船潜艇等结构及部件，其振动特性决定着结构的舒适性、安全性和可靠性。其中，复杂组合结构的中高频振动分析作为研究的热点和难点至今仍不成熟。动刚度法以其精确高效性已被用于全频域的模态和动态响应分析，但仅局限于梁杆结构或对边简支单方向组合的板壳结构。本项目以任意边界条件下多种复杂组合形式的梁板壳组合结构为研究对象，建立全频域高精度的谱动刚度解析模型；研究对应的改进Wittrick-Williams模态分析算法，探索结合谱动刚度法和线性变换的动态响应分析算法，并进一步提高算法的运算效率；将算法运用到列车复合夹层板、机翼翼盒等工程结构并进行数值及试验验证。本项目预期为复杂组合结构的声振参数分析和优化设计提供一套准确、高效、可靠的全频域振动分析程序，为其它振动分析方法提供基准解和关键参数，具有极其重要的科学研究意义和工程实用价值。

复杂梁板壳组合结构被广泛运用于高速列车、航空航天、舰船潜艇等结构，其中高频振动分析作为研究的热点和难点至今仍不成熟。动刚度法以其精确高效性已被用于全频域的模态和动态响应分析，但仅局限于梁杆结构或对边简支单方向组合的板壳结构。本项目以任意边界条件下多种复杂组合形式的梁板壳组合结构为研究对象，在动刚度解析建模方法、模态/响应分析算法及工程应用方面开展了较为系统的工作，极大拓展了方法的工程适用范围。在解析建模方法方面：1）建立了多种刚体、一、二维柔性体单元的动刚度解析模型，丰富了动刚度单元库，包括：Rayleigh-Bishop和Mindlin-Hermann杆单元、变截面/功能梯度梁单元、弹性地基上非局部纳米梁、任意经典/非经典边界下二维膜、任意经典/非经典边界下二维板（振动和屈曲）、功能梯度碳纳米管增强复合锥形壳等单元。2）提出了多种不同类型单元组合的解析建模方法，包括：任意刚体-梁组合的多体动力学模型、任意截面梁加筋板模型、一维单元（点节点）与二维单元（线节点）组合模型、考虑参数不确定性的膜组合结构、边界/连接不确定性的板组合结构等的建模方法，同时建立了表征点阵/蜂窝材料动力学参数的解析模型。在模态分析和响应算法方面：针对以上的所有动刚度解析单元及不同类型单元组合模型，提出了相应模态Wittrick-Williams（WW）算法中全固支模态计数（J0）的解析表达式，提出了针对随机动刚度模型的扩展WW算法和针对一-二维单元组合模型的改进WW算法；探索了结合动刚度法和线性变换的动态响应分析算法。工程应用方面：已将算法运用到列车地板、车体、转向架构架、受电弓、船舱舱段等工程结构并进行数值验证，充分证明了该方法在全频段的高效精确性。本项目为复杂组合结构的声振参数分析和优化设计提供一套准确、高效、可靠的全频域振动分析程序，具有非常重要的科学研究意义和工程实用价值。