摘要
在航空航天领域，随着多体系统柔性附件尺寸的弹性变形的增大，转速的加快，运行精度要求的提高，系统的动力学性态越来越复杂，系统的刚—柔耦合效应也越来越显著，需要引起工程界的重视。如卫星天线、太阳帆板、风力发电机的桨叶等，在太阳辐射、风力和构件本身的惯性力等外界环境因素的综合作用下，这些复杂构型柔性构件的弹性变形对大范围运动的影响更为显著。曲梁和板壳结构作为这些复杂结构多体系统中的常用部件，建立其多体系统的动力学模型对于准确预测现代工程中多体系统的力学行为有重要的工程价值。
为了解决曲梁和板壳结构多体系统的计算精度和计算效率问题，本文提出了一种基于弧坐标的刚—柔耦合动力学建模方法，采用三类坐标系：惯性坐标系、浮动坐标系和曲线坐标系对柔性体上任意点的位形进行描述，用弧坐标取代笛卡尔坐标，描述了曲梁上任意点的弹性变形，建立了曲梁上任意点的运动学关系。在此基础上考虑几何非线性，从曲梁的格林应变关系式出发推导了变曲率曲梁的应变和位移关系式，用曲梁单元取代直梁单元，建立了适用于变曲率曲梁的有限元离散的刚-柔耦合动力学模型。首次开展了柔性曲梁的刚—柔耦合动力学实验，将曲梁重力摆的刚—柔耦合动力学仿真结果与实验结果进行对比验证了本文几何非线性建模理论的正确性，并通过仿真算例研究了几何非线性项对刚—柔耦合动力学特性的影响。将本文曲梁单元的仿真计算结果与直梁逼近单元的仿真计算结果进行比较，验证了本文曲梁单元模型的快速收敛性和有效性。
在曲梁多体系统动力学建模理论研究的基础上进一步研究柱状壳结构多体系统的几何非线性动力学建模方法。引入曲线坐标系描述柱状壳结构的弹性变形，采用二维的壳单元进行离散，创新性地推导了适用于任意形状柱状壳的具有程式化特征的广义弹性力阵，缩减了计算规模，避免了大型非线性刚度阵的计算，有利于广义弹性力阵关于广义坐标的导数阵的高效计算。通过对重力作用下气浮台-柱状壳和气浮台-矩形板的刚—柔耦合动力学实验验证了几何非线性建模理论的正确性，指出了传统的基于线弹性理论的建模方法处理大变形刚—柔耦合动力学问题的不足，并对壳单元应变计算的收敛性进行分析。
进一步考虑了材料的各向异性，建立给定热载荷作用下复合材料壳结构多体系统的几何非线性动力学模型。研究了热变形和几何非线性效应对板壳结构多体系统刚—柔耦合动力学特性的影响。为了能更有效地将本文的热载荷作用下刚—柔耦合动力学建模理论研究与工程实际结合，考虑刚体姿态运动、弹性变形和温度变化的相互耦合，首次建立了热流密度与刚体姿态坐标和弹性坐标的精确关系式，提出了刚-柔-热三者耦合的动力学建模方法。通过仿真算例对刚—柔-热耦合的动力学机理进行分析，成功地解释了刚—柔-热耦合引起的热振动现象。
为了解决长期存在的几何非线性刚—柔耦合多体系统动力学方程数值计算效率低的问题，基于本文弹性力阵的程式化的推导方式，提出了增量法，创新性地推导非线性广义弹性力阵关于多体系统广义坐标导数阵，实现了柔性多体系统刚—柔耦合动力学方程的高效、精确的数值仿真。
最后对全文研究工作进行总结，指出了本文的主要创新点。
In the research field of aerocraft and spacecraft, with the increase of the elasticdeformation, the rotating speed and the operational accuracy of the flexible appendage,the system dynamic behavior becomes more and more complicated, and the rigid-flexiblecoupling effect becomes more and more significant, which should be paid attention in theengineering application. Influenced by the combined action of environmental factorssuch as solar radiation, wind force and body inertial force, the large overall motion ofsatellite antenna, the solar panel and wind turbine blade are more easily affected by theelastic deformation of flexible appendage. It has important value to establish themultibody system dynamic equations for curved beam and plate shell structures whichare basic components of those complicated mechanical systems in order to accuratelypredict the dynamic behavior of the system.
In order to improve the computational accuracy and efficiency for dynamics ofcurved beam and shell flexible multi-body system, the dynamic modeling method ofrigid-flexible coupling system based on arc coordinates is proposed, in which threereference frames (global frame, floating frame, and curvilinear frame) are used todescribe the configure of arbitrary point in the flexible body. Arc coordinate areintroduced instead of previous Cartesian coordinates for describing the elasticdeformation, and the kinematics relationship of an arbitrary point of the curved beam isestablished. Based on Green strain of spatially varying curvature beam, the nonlinearstrain-displacement relationship for plane beam with varying curvature is derived. Finite element method is used for discretization. Instead of using the previous straight beamelements, curved beam elements are proposed to approximate the curved beam withvarying curvature. Rigid-flexible coupling dynamic equations are obtained, which aresuitable for the curved beam undergoing large overall motion. For validation the presentmodeling theory, the experimental tests for curved beam pendulum are carried out for thefirst time. By comparing the experiments results and those of present linear and nonlinearmodel, the correctness and accuracy of present nonlinear model are verified. Comparisonof the simulation results obtained by linear and nonlinear models show the geometricnonlinear effect. Furthermore, comparison of the simulation results obtained by thecurved beam elements and straight beam elements verifies the quick convergence andhigh efficiency of the curved beam element.
Based on the research of the curved beam, the rigid-flexible coupling dynamicequations of the cylindrical shell are established. Arc coordinates are employed todescribe the deformations, and2-D shell element is adopted for finite elementdiscretization, and then a new method for evaluating the generalized elastic forces, whichis more formalized and more easily used than the previous method, therefore, the largecalculation quantity of nonlinear stiffness matrix is avoided, and the simulation cost isreduced obviously. Great advantages can be also achieved from the present evaluation ofthe elastic forces when calculating the jacobian of the elastic forces. By the experimentof the single axis air-bearing test bed and plate structure rigid-flexible system, thecorrectness and accuracy of present nonlinear model are verified and the shortcoming oftraditional linear model is pointed out for dealing with large deformation rigid-flexibleproblem.
Considering the anisotropic material and thermal effect, rigid-flexible couplingdynamic equation is build for composite shell considering thermal shock. The thermaldeformation and geometrical nonlinear effect on the rigid-flexible coupling dynamics are studied. In order to further apply the present rigid-flexible coupling dynamics modelingtheory in the engineering field, the relationship among the heat flux density and theattitude motion coordinates as well as the elastic coordinates is firstly established.Considering the coupling among the attitude motion, structural deformations andtemperature change, rigid-flexible-thermal coupling dynamic modeling method isproposed. The rigid-flexible-thermal coupling dynamic performance is analyzed bymumerical simulation, which can be used for explanation of the thermally inducedfluttering phenomena.
Based on the formulation of evaluating the generalized elastic forces, a newincremental method is proposed, and jacobian of the elastic forces are derivedinnovatively. Efficient and accurate simulations of rigid-flexible coupling dynamicsystem are achieved by the present incremental method.
Finally, the research work is summarized and the contributions of the presentinvestigation are concluded.
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