【作者】 李莉；

【导师】 洪嘉振； 刘铸永；

【作者基本信息】 上海交通大学 ， 一般力学， 2015， 硕士

【摘要】 浮动坐标系方法是柔性多体系统动力学最常用的方法,其中柔性体的运动被分成两部分:用浮动坐标系描述的大范围刚体运动和相对于浮动坐标系的小幅弹性变形。有限单元法被广泛的采用来描述复杂柔性体的弹性变形,导致建立的动力学模型的自由度数目庞大,动力学方程求解耗时过长,甚至出现无法求解的现象。如何降低柔性体的自由度,是当前柔性多体系统动力学研究的一个重要命题。因此,为了提高柔性多体动力学仿真的计算效率,便于控制设计和实施,就必须要对柔性多体系统动力学模型降阶进行研究。借鉴内平衡理论,提出了一种Krylov子空间方法的阶数自动控制算法。在阅读大量中英文文献的基础上,对现有的柔性多体动力学模型降阶方法,特别是模态降阶法和Krylov子空间法进行了较为全面的综述。系统地给出了一阶Krylov子空间法和二阶Krylov子空间法的理论推导过程。详细介绍了现有的Krylov子空间自动降阶算法。受内平衡模态降阶方法的启发,本文提出了一种基于Hankel奇异值的Krylov阶数自动控制算法。当前常用临界投影角度法来实现阶数自动控制,然而Krylov子空间法降阶模型的准确性和阶数对临界角度的取值相当敏感,相对于该算法,本文提出的阶数控制方法比较容易实现阶数的准确控制。基于Krylov子空间法及所提阶数控制方法,研究了柔性多体动力学模型降阶问题。通过与当前常用的模态降阶方法,如模态截断方法、模态价值分析方法、内平衡方法比较,研究Krylov子空间方法及所提阶数控制方法的正确性和高效性。研究结果表明无论是否考虑大范围运动(低速运动)的影响,相对于模态降阶方法,Krylov子空间方法只需要较低的自由度就可以得到和采用有限元方法完全一致的结果。说明该方法能够保持所关注的系统的低频和高频动力学特性,并且具有较高的计算效率。结合多变量方法,将Krylov子空间法成功应用于柔性多体系统接触碰撞问题的模型降阶。柔性多体系统的接触碰撞过程是不连续、高瞬态和高度非线性的,无法直接应用模型降阶。多变量方法将柔性体分为碰撞区和非碰撞区,碰撞区采用有限元描述,非碰撞区采用模态描述,从而使得模型降阶的成为可能。研究结果表明,相对于模态降阶方法,Krylov子空间法可以更大程度地缩减非碰撞区域的自由度数,进而提高动力学全局仿真的效率。更多还原

【Abstract】 The floating frame method is most commonly used in flexible multi-body systems, in which the flexible body’s motion is subdivided into two parts: a large overall reference motion and elastic deformations with respect to the floating frame. The finite element method is widely used to describe the elastic deformations of flexible bodies, which leads to a large number of elastic coordinates and large computational burden. Thus, model reduction is investigated in this paper to improve the computational efficiency of flexible multi-body dynamic simulations. Moreover, it makes control easier to be designed and implemented.Inspired by balance truncation method, this dissertation proposes a new automatic order control algorithm based on Hankel singular value. The existing model reduction methods of flexible multi-body system, especially modal reduction method and Krylov subspace method are comprehensively reviewed. Furthermore, both first order Krylov subspace equations and second order Krylov subspace equations are derived systematically. The existing automatic reduction algorithms are introduced in detail. Then, inspired by balance truncation method, this dissertation proposes a new automatic order control algorithm based on Hankel singular value. The critical projection angle algorithm is usually used to implement order control of Krylov subspace method. However, the size and accuracy of the reduced model are sensitive to the value of critical projection angle, and comparing with the existing critical projection angle method, the physical meaning of the new method which is proposed in this dissertation is clear. In addition, it’s easier to realize order control.Research on model reduction of flexible multi-body dynamic systems is carried out based on Krylov subspace method. Compared with the existing modal reduction method such as modal truncation method, modal cost analysis method and balance truncation method, with the Krylov subspace method smaller orders are needed whether the influence of large overall reference motion is taken account or not, which is in good agreement with that of the finite element method. It means that Krylov subspace method can keep both low frequency characteristics and high frequency characteristics of flexible dynamic systems and its simulation efficiency is higher. Combined with multi-variable method, Krylov subspace method is successfully applied to model reduction of multi-body system’s contact-impact area. The contact-impact process is discontinuous, high transient and high nonlinear, model cannot be reduced directly. Multi-variable method divides the flexible body into two parts: impact area and non-impact area. The deformations of impact area are described by finite element coordinates and the deformations of non-impact area are described by modal coordinates. And the subarea description makes model reduction possible. The numerical simulations show that Krylov subspace method can reduce more degrees-offreedom of the non-impact area and the simulation efficiency is improved a lot.更多还原