基于隧穿理论和高级统计能量分析的加筋板振动特性和减振机理研究

Periodically rib-stiffened plates are widely used in engineering equipment where structural vibration can significantly affect the performance of the equipment and therefore it is of great importance to study the vibration transmission properties and vibration reduction of rib-stiffened plates. Statistical Energy Analysis (SEA) is well suited for the prediction of structural dynamic response in mid- and high-frequency range, however, when dealing with periodic structures like stiffened plates, predominant limitations can occur. In order to solve this problem, the concept of tunneling mechanism from quantum mechanics is introduced into the classic SEA to describe the physical processes of energy conservation, transmission and dissipation in the structural systems and by incorporating Ray Tracing theory and Matrix Update theory in SEA, this project will study the improvement of classic SEA and aim to provide an efficient and accurate method for the prediction of dynamic response in mid- and high-frequency range. Base on this method, this project will then study the vibration transmission properties and vibration reduction of rib-stiffened plates and also coupled systems with stiffened plates connected to other plates/beams. This project will then investigate the effects of material and structural properties, structure coupling condition and vibration transmission path on the dynamic response of the coupled systems. Furthermore, with the aim of vibration reduction on the stiffened plates, this project will analyze the mutual influence mechanisms between the frequency band gap properties of stiffened plate and the vibration response of the coupled system and identify the key influential factors. Finally, experimental specimen will be designed and tested to validate the theory. The outcome of the project will be able to provide new theory foundation and technique support for vibration analysis and vibration reduction design for engineering rib-stiffened plates.

周期加筋板广泛应用于工程装备中，其振动问题是影响装备性能的重要因素，因此，开展加筋板振动特性和减振机理研究具有重要意义。用于预报复杂系统动力学响应的统计能量分析法在处理加筋板中、高频振动响应时有一定优势，但同时存在很大局限。针对这一问题，项目拟将量子物理领域中隧穿效应的概念引入经典统计能量分析方法中，描述系统中能量存储、传递和耗散的物理过程，进而应用射线追踪理论和矩阵更新算法，改进经典统计能量分析法，建立中高频振动响应的精确预报平台。在此基础上，以周期加筋板及周期加筋板与梁/板连接构成的耦合系统为对象，研究加筋板在不同结构耦合形式、多波场耦合、多振动传递路径下的振动特性。进一步，以结构减振为目标，研究加筋板带隙减振特性和耦合系统振动特性的相互影响规律和调控机理，提取关键因素。最后，设计实验样件，完成实验测试与验证。项目研究成果有望为加筋板振动特性分析和减振设计提供新的理论基础与技术支撑。

周期加筋板广泛应用于工程装备中，其振动问题是影响装备性能的重要因素，因此，开展加筋板振动特性和减振机理研究具有重要意义。用于预报复杂系统动力学响应的统计能量分析法在处理加筋板中高频振动特性时有一定优势，但同时存在很大局限。研究发现，经典统计能量法在处理加筋板振动响应问题时可产生较大误差，造成这一问题的原因是经典方法未能考虑加筋板对弯曲波的滤波效应。针对这一问题，本课题将量子物理领域中隧穿效应的概念引入经典统计能量分析方法中，描述系统中能量存储、传递和耗散的物理过程，进而应用射线追踪理论和矩阵更新算法，改进经典统计能量分析法，建立中高频振动响应的精确预报平台。在此基础上，以周期加筋板及周期加筋板与板连接构成的耦合系统为对象，研究加筋板在不同结构耦合形式、多波场耦合、多振动传递路径下的振动特性。理论与实验结果表面，建立的高级统计能量法在计算加筋板及加筋板耦合系统振动响应时，可以显著提高预报精度，从而克服经典问题局限。进一步，以结构减振为目标，研究加筋板带隙减振特性和和基于局域共振周期加筋板的带隙减振设计，深入分析减振机理和调控参数，提取关键因素。最后，设计实验样件，完成实验测试与验证。项目研究成果有望为加筋板振动特性分析和减振设计提供新的理论基础与技术支撑。