含局部非线性的月球探测器软着陆动力学模型降阶分析

为准确预估探测器着陆冲击过程的动力学响应，采用非线性有限元方法建立了探测器软着陆动力学模型，能够较全面地反映出各种非线性因素。针对非线性有限元求解耗时长的弱点，考虑到探测器的局部非线性特性，利用广义动力缩聚（GDR）方法建立了月球探测器中心体的降阶模型。提出了一种基于脉冲响应函数的模态截断准则，在广义动力缩聚方法的基础上筛选少数几阶模态影响系数（MIC）较高的模态表征中心体的加速度响应，能够进一步降低模型的阶数。将降阶的中心体模型与含非线性的缓冲机构连接后进行的软着陆动力学分析能够准确而快速地预估探测器测点的加速度响应，与非降阶模型对比，计算时间缩短了75.5%，加速度响应的相对峰值误差控制在5%以内。数值仿真表明，广义动力缩聚方法能够有效地解决传统非线性有限元方法求解效率低的问题，本文所提模态截断准则的优点是适于求解模态密集问题并且与系统的输入输出无关。

Model Reduction Analysis of Soft Landing Dynamics for Lunar Lander with Local Nonlinearities

In order to accurately predict the dynamic response of a lunar lander during its landing process, a dynamics model for the lunar lander is built using the nonlinear finite element method. This method considers comprehensively various nonlinear factors but is time consuming. Aiming at solving this disadvantage, the generalized dynamic reduction (GDR) method is adopted to build an order reduced model for the center body of the lunar lander which takes into consideration the lander's local nonlinearities and a new modal truncation criterion is proposed based on the impulse response function. By means of this criterion, the acceleration of the center body can be characterized by selecting just a few normal modes with high model influence coefficient (MIC) based on GDR method, this further reduces the order of the center body. In a case study on soft landing dynamics, the order reduced center body is jointed with the nonlinear landing gear. Compared with the original non-reduced FE model, up to 75.5% computational time is saved using the modal truncation criterion while the relative peak error of acceleration is kept below 5%. From the results it can be concluded that the GDR method works excellently for enhancing the simulation efficiency of lunar landing and the proposed criterion has the advantage of solving modal-denseness systems with independence of input and output.