可伸缩悬臂复合材料层合板的时变非线性动力学研究

The deployable-and-retractable composite laminated cantilever plates are being widely used in many engineering fields like aerospace engineering and robotics, etc. This kind of structure is characterized by time-varying length, and its transversal vibration might be triggered quite easily by the axially moving of the structure itself. When subjected to the external loads, the nonlinear vibrations and instabilities of the deploying-and-retracting composite laminated cantilever plates might occur easily, and that will cause significant economy loses. However, the time-varying nonlinear dynamic characteristics of the plate during the deploying and retracting process are not fully understood, which is one of the main factors that restrain the application and development of the structures. In the present project, we will conduct the basic research on the time-varying nonlinear dynamic responses of a deploying-and-retracting composite laminated cantilever rectangular plate subjected to several external excitations on the basis of the telescopic wings. The main contents of this project are as follows: The nonlinear dynamics modeling for the deployable-and-retractable cantilevered laminated composite plates subjected to the external excitations; Research on the time-varying nonlinear vibration characteristics of the plate during the deploying-and-retracting process, and investigate about the analytic solution of the time-varying parameter differential equations; Based on the piezoelectric materials, the theoretical research on the nonlinear vibration suppression for the deploying-and-retracting process is carried out. This project is intended to analyze the time varying nonlinear dynamic phenomena during the deploying and retreating process for the composite laminated cantilever plates and reveal the mechanism of complex nonlinear dynamic behaviors for the time-varying structures. This research will provide the theoretical support to the engineering problem of the time-varying structures in the aviation industry.

可伸缩悬臂复合材料层合板结构在航空航天和机器人等工程领域已有应用。这种展长随时间变化的轴向运动容易诱发结构的横向振动，在外部载荷的作同下，更易发生大振幅的非线性振动及失稳，引起重大损失。目前，人们尚未完全清楚其外伸与收缩过程中的时变非线性动力学特性及运动规律，成为制约这类结构广泛应用的主要因素之一。本项目以航空领域中可变体机翼的伸缩变形过程为研究对象，对可伸缩悬臂复合材料层合板的时变非线性振动进行基础理论研究。建立外载荷作用下可伸缩悬臂复合材料层合板的时变系数非线性动力学模型；研究时变系数非线性动力学方程的解析求解及时变非线性振动特性；基于压电材料开展可伸缩悬臂压电复合材料层合板的非线性振动抑制方案研究。分析可伸缩悬臂复合材料层合板在外伸与收缩变形过程中的非线性动力学现象，揭示时变结构复杂非线性动力学行为产生的机理，同时为航空领域中时变结构的工程问题提供理论支持。

轴向可伸缩悬臂复合材料层合板结构在外载荷作用下极易发生复杂的非线性动力学形为，影响时变结构在工程中的安全应用。本项目主要研究不同外载荷作用下可伸缩悬臂复合材料层合板在外伸和收缩变形过程中的时变非线性动力学特性,揭示时变结构发生复杂动力学行为的机理。课题在以下几个方面取得了进展：(1) 研究了线性和非线性气动载荷作用下可伸缩悬臂复合材料层合板的非线性动力学建模；选取了与时间有关的模态函数对方程进行二阶离散分析。(2) 采用一阶和高阶剪切理论建立了复合材料悬臂层合板的时变系数动力学模型，采用改进的多尺度方法进行了解析研究。(3) 建立了轴向可伸缩压电复合材料层合板的非线性动力学模型，基于压电材料开展了可伸缩悬臂复合材料层合板的非线性振动抑制研究。(4) 设计和搭建了简易轴向可变长度的悬臂板结构并开展了动力学实验研究。本项目研究结果将为工程领域中时变结构的设计和应用提供理论依据。