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首页> 外文会议>International Conference on Mechanical Engineering and Mechanics vol.1; 20051026-28; Nanjing(CN) >Dynamics Modeling for a Rigid-flexible Coupling System with Nonlinear Deformation Field
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Dynamics Modeling for a Rigid-flexible Coupling System with Nonlinear Deformation Field

机译：具有非线性变形场的刚柔耦合系统动力学建模

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摘要

In this paper, a moving flexible beam, which incorporates the effect of the geometrically nonlinear kinematics of deformation, is investigated. Considering the second-order coupling terms of deformation in the longitudinal and transversal deflections, the exact nonlinear strain-displacement relations for a beam element are described. The shearing strains formulated by the present modelling method in this paper are zero. So, it is reasonable to use geometrically nonlinear deformation fields to demonstrate and simplify a flexible beam undergoing large overall motions. Then, considering the coupling terms of deformation in two dimensions, finite element shape functions of a beam element and Lagrange's equations are employed for deriving the coupling dynamical formulations. The complete expression of stiffness matrix and all coupling terms are included in the formulations. A model consisting of a rotating planar flexible beam is presented. Then the frequency and dynamical response are studied in the end. Numerical examples demonstrate that a 'softer beam' can be obtained, when the more coupling terms of deformation are added to the longitudinal and transversal deformation field. The natural frequencies of the present model in this paper are lower than that of one-order coupling model, but they all increase when the angular velocity of the beam is increased. When the joint trajectory of the beam is uncertain, because of the coupling effect of rotation and deformation, the difference between two models is not distinct. When the joint trajectory of the beam is known, the simulation illustrates that the beam tip deflection of geometrically nonlinear dynamical model in this paper is larger than that of one-order coupling dynamical model which only considers the second coupling terms of deformation in the longitudinal deflection, especially, when the model has initial deformation. The traditional zero-order and one-order model may not provide an exact dynamic model in some cases.
机译：在本文中，研究了一种移动柔性梁，该柔性梁结合了变形的几何非线性运动学的影响。考虑到纵向和横向挠度中变形的二阶耦合项，描述了梁单元的精确非线性应变-位移关系。本文采用目前的建模方法确定的剪切应变为零。因此，使用几何非线性变形场来演示和简化经历大的整体运动的柔性梁是合理的。然后，考虑二维的变形耦合项，采用梁单元的有限元形状函数和拉格朗日方程来推导耦合动力学公式。刚度矩阵的完整表达式和所有耦合项都包含在公式中。提出了一个由旋转平面柔性梁组成的模型。然后对频率和动力响应进行了研究。数值算例表明，当将更多的耦合变形项添加到纵向和横向变形场时，可以获得“较软的梁”。本文模型的固有频率低于一阶耦合模型的固有频率，但是当光束角速度增加时，它们的固有频率都会增加。当梁的关节轨迹不确定时，由于旋转和变形的耦合作用，两个模型之间的差异并不明显。当已知梁的联合轨迹时，仿真表明，本文的几何非线性动力学模型的梁尖端挠度要大于一阶耦合动力学模型的一阶耦合动力学模型，后者仅考虑纵向挠度中的第二个耦合变形项。 ，尤其是当模型具有初始变形时。在某些情况下，传统的零阶和一阶模型可能无法提供精确的动态模型。

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