复合材料点阵夹芯板的非线性动力学特性及共振机理研究

Composite truss core sandwich structures have great potential for applications in aerospace field and the large amplitude vibration is one of the important factors for the malfunction and damage of the aerospace vehicles. This project aims to study the large amplitude nonlinear vibration of the composite truss core sandwich plate in aerospace environment. The research contents mainly include: The governing equations of motion which can more accurately describe the actual elastic deformation of the composite truss core sandwich plate will be derived based on an improved sandwich panel theory; considering the different truss core configurations, physical and excitation parameters, the key problems such as the influences of the vibration states on the softening/hardening nonlinearities and the energy transfer between the different modes of the composite truss core sandwich plate will be studied through theoretical analysis and numerical method; the global bifurcations and multi-pulse chaotic dynamics of the composite truss core sandwich plate will be also investigated by the extended Melnikov method, and the key parameters which influence the vibration responses and its thresholds will be obtained. The research emphases of this project are to summarize the laws of the nonlinear vibration and chaotic motion of the composite truss core sandwich plate and to analyze the internal relations and generation mechanism of the different resonance phenomena. The research results not only can play an important role in guiding design, selection and vibration control of the composite truss core sandwich structures in aerospace field, but also can promote the development of the theoretical research of nonlinear dynamics.

复合材料点阵夹芯结构在航空航天领域中具有巨大的应用潜力，而大幅振动是飞行器产生故障及损毁的重要原因之一。本项目针对航空航天环境中复合材料点阵夹芯板的大幅非线性振动特性进行深入研究，研究内容主要包括：改进现有夹芯板理论，建立能够更加精确地描述复合材料点阵夹芯板实际弹性变形的动力学方程；通过理论和数值方法，考虑不同的芯层构型、结构物理参数和激励参数，研究振动状态对软/硬非线性特性和模态间能量传递方式的影响等关键问题；利用广义Melnikov方法研究点阵夹芯板的全局分叉和多脉冲混沌动力学，获得影响点阵夹芯板复杂振动响应的关键参数及其临界值。研究重点在于总结复合材料点阵夹芯板非线性振动及混沌运动的规律，分析各种共振现象的内在联系及产生机理。研究结果不仅能够对复合材料点阵夹芯结构在航空航天领域中的设计、选用及振动控制起到重要的指导作用，还可以在一定程度上推动非线性动力学理论研究的发展。

复合材料点阵夹芯结构正越来越多地应用于航空航天领域，因此，大幅非线性振动是该类结构在应用过程中需要面临的问题。本项目中，分别基于经典板理论、一阶剪切变形理论、三阶剪切变形理论和折线理论计算出复合材料点阵夹芯板的固有频率，分析了不同建模理论的适用范围，探讨了折线理论在研究点阵夹芯结构动力学特性方面的优越性。研究了点阵夹芯板固有频率随着复合材料蒙皮铺层、芯层高度、杆件半径和杆件倾角的变化情况。利用折线理论建立了复合材料点阵夹芯板的非线性动力学方程。研究了点阵夹芯板的主共振、亚谐共振、超谐共振和内共振响应，分析了结构参数对非线性响应和硬特性非线性的影响，分析了内共振发生时点阵夹芯板两阶模态间的能量传递方式。研究了点阵夹芯板在不同内共振条件下的周期运动、全局分叉和混沌运动，给出了点阵夹芯板产生周期运动的参数域，分析了系统运动状态随激励幅值的变化规律。此外，根据研究中遇到的问题，探索性地研究了含呼吸裂纹的点阵夹芯梁的动力学特性和裂纹识别方法以及基于靶向能量转移原理的点阵夹芯结构的非线性振动控制方法。本项目的研究结果能够对复合材料点阵夹芯结构的设计、选用及振动控制起到重要的指导作用和数据支持。