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A recursive formulation for the dynamic analysis of open-loop deformable multibody systems.

机译：用于动态分析开环可变形多体系统的递归公式。

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摘要

A recursive nonlinear lagrangian formulation for the spatial kinematic and dynamic analysis of open chain mechanical systems containing interconnected deformable bodies, each of which may undergo large translational and rotational displacements, is developed. While approximation techniques such as the finite element, Rayleigh-Ritz methods, or experimentally identified modal parameters can be used to introduce the elastic coordinates that describe the deformation of the bodies with respect to selected body references, the large relative motion between the neighboring deformable bodies are described by the large relative translational and rotational displacements between a set of intermediate coordinate systems using a minimum set of relative translational and rotational coordinates. The nonlinear terms that represent the dynamic coupling between the large relative motion and the small elastic deformations are identified and presented in terms of a set of time-invariant quantities that depend on the assumed displacement field. These sets of invariant matrices provide a systematic approach to study the spatial dynamics of open loop kinematic chains. The system differential equations are developed in terms of these invariants using Lagrange's equation of motion.; In order to demonstrate the potential use of the nonlinear recursive formulation proposed in this thesis, a computer algorithm is developed and used to determine the nonlinear vibration response of a coupled rotor-fuselage system of a helicopter model. This displacement of the deformable rotor is expressed in terms of a set of mode shapes obtained using the finite element method. The differential equations of motion are expressed in terms of a coupled set of relative joint variables and modal elastic coordinates. These equations are integrated forward in time using a direct numerical integration method. Two cases are considered. In Case A, the rotor lies in a plane normal to the rotor axis of rotation while in Case B, it is assumed that the rotor has built in coining angle at its inner attachment point. It is shown that the elastic rotors are in general stiffer in the in-place direction (Case A) than in out-plane direction and the natural frequencies are correspondingly higher. By comparing the two cases, it is also concluded that decreasing the coining angle of the blade as well as design of the rotor blades so that their mass is confined to the plane of rotation leads to a more stable solution. It is also shown that by adding damping, a more stable coupled rotor-fuselage system can be achieved.
机译：提出了一种非线性非线性拉格朗日公式，用于包含相互连接的可变形体的开链机械系统的空间运动学和动力学分析，每个变形体都可能经历较大的平移和旋转位移。虽然可以使用诸如有限元，Rayleigh-Ritz方法或实验确定的模态参数之类的近似技术来引入弹性坐标，该弹性坐标描述相对于选定的实体参考来描述实体的变形，但相邻可变形实体之间的相对运动较大通过使用最小的一组相对平移和旋转坐标之间的一组中间坐标系之间的较大的相对平移和旋转位移来描述这些变量。识别和表示代表大的相对运动和小的弹性变形之间的动态耦合的非线性项，并根据一组假定的位移场随时间变化的量进行表示。这些不变矩阵集为研究开环运动学链的空间动力学提供了一种系统的方法。使用拉格朗日运动方程根据这些不变量来开发系统微分方程。为了证明本文提出的非线性递归公式的潜在用途，开发了一种计算机算法并将其用于确定直升机模型的旋翼-机身耦合系统的非线性振动响应。可变形转子的这种位移用使用有限元方法获得的一组模态形状表示。运动的微分方程用相对关节变量和模态弹性坐标的耦合集表示。使用直接数值积分方法将这些方程式及时向前积分。考虑了两种情况。在情况A中，转子位于垂直于转子旋转轴线的平面中，而在情况B中，假定转子在其内部连接点处具有精压角。结果表明，弹性转子在原位方向（情况A）上通常比在外平面方向上更刚性，并且固有频率相应地更高。通过比较这两种情况，还得出结论，减小叶片的精压角以及减小转子叶片的设计，以使它们的质量限制在旋转平面内，会导致更稳定的解决方案。还显示出，通过增加阻尼，可以实现更稳定的转子-机身耦合系统。

著录项

  • 作者

    Changizi, Koorosh.;

  • 作者单位

    University of Illinois at Chicago.;

  • 授予单位 University of Illinois at Chicago.;
  • 学科 Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 1990
  • 页码 154 p.
  • 总页数 154
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 机械、仪表工业;
  • 关键词

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