【作者】 颜世军；

【导师】 刘占芳；

【作者基本信息】 重庆大学 ， 工程力学， 2011， 博士

【摘要】 在旋转机械、航空航天、车辆工程、柔性机械臂以及现代微机电系统(MEMS)等领域中含有各种结构形式的变形体,由这些构件组成的单体或多体系统在历经大范围刚体运动的同时发生自身的变形,运动与变形耦合产生的附加的惯性力将对结构动力学特性和响应产生重要影响,为此大范围运动下变形体刚柔耦合动力学研究对促进这些领域结构动力分析、系统设计与控制技术的发展等都至关重要。运动与变形耦合理论涉及到刚体动力学与变形体力学的统一,要求所建立的耦合动力学模型既能反映刚柔耦合效应,又能在无刚体运动的时候退化为变形体力学,而在不变形的时候退化为刚体动力学。目前对刚柔耦合动力学的研究集中在力学建模、数值求解、多体系统下的接触与碰撞以及多物理场下的刚柔耦合效应等领域,然而由于刚柔耦合动力学涉及刚体运动与弹性变形的统一描述,且具有运动非线性和几何非线性效应,这些问题的解决至今尚不圆满,且随着广义弹性理论的发展,在基于广义弹性理论的基础上研究变形体的刚体运动与变形耦合问题尚较少涉及。单体运动与变形耦合动力学研究是柔性多体动力学研究的基础,在分析国内外对柔性多体动力学以及广义弹性力学研究现状的基础上,本文集中关注离心环境下结构的运动与变形耦合理论建模和数值算法开发,引入了含有三个材料参数的广义弹性体模型,采用广义弹性体模型分析了不同尺度下结构的静力和动力特性,建立了离心环境下广义弹性体的运动与变形耦合动力学模型并开发了相应的数值算法,考察了离心环境下典型悬臂梁结构的动力特性。论文的主要工作和结论如下:①考虑含旋转变形的广义弹性体,在偶应力弹性理论和微极弹性理论的研究基础上,确定动量和动量矩守恒方程形式和广义弹性体的运动学表达。应用虚功原理和各向同性张量函数定理,改进偶应力和曲率张量的本构关系。建立广义弹性体的动力学方程和含力偶的初边值条件。②采用约束变分原理,考虑位移和转角为独立变量,采用罚方法引入约束条件,建立广义弹性体的有限元控制方程。构造了4结点12自由度的平面等参元和8结点48自由度的六面体等参元。对平面单剪问题和悬臂梁静力和动力分析表明广义弹性体模型能够把经典弹性理论的应用范围扩展到微观领域,且在力学分析时给出了更加丰富的信息,有利于结构分析,能够计及尺寸效应的影响。③建立了简化的双自由度弹簧质量系统的耦合动力学分析模型。利用简化的双自由度弹簧质量系统,引入描述质点刚体旋转运动和变形运动的惯性坐标系和浮动坐标系,应用正交张量和欧拉罗德里格斯旋转公式,给出质点在惯性坐标系和浮动坐标系的速度和加速度表达,建立定轴旋转的离心环境下的动力学模型,对典型算列的计算结果表明离心力效应、科式力效应和偏心效应对转动系统的动力特性有重要影响。④建立了定轴变速离心环境下的广义弹性体的运动与变形耦合动力学方程。解析浮动标架下的离心力、科氏力、切向惯性力,基于连续介质力学分析方法,在浮动坐标系下建立广义弹性体动量和动量矩守恒方程。应用广义弹性体关于应力和偶应力的本构关系,给出浮动坐标系下含力偶的初边值条件,建立离心场中广义弹性体运动与变形耦合动力学方程,并采用初应力法解析了柔性结构的动力刚化效应。⑤开发离心环境下广义弹性体运动与变形耦合动力学问题的数值算法。利用虚功原理建立广义弹性体运动与变形耦合的有限元方程,采用8结点48自由度的六面体等参元对广义弹性体进行离散。解析柔性结构由于几何非线性带来的动力刚化效应,考察广义惯性力形式,建立广义弹性体运动与变形耦合动力分析的有限元控制方程。⑥将梁视为广义弹性体,针对尺寸和几何特征不同的梁型结构,应用所建立的广义弹性体有限元控制方程,数值求解梁型结构在恒速和变速的离心环境下的动频及动力响应特性,结合挠度和强度两方面考察了离心场下旋转梁的临界转速。研究结果表明科式力和离心力效应取决与转速、结构形态以及旋转姿态,旋转姿态影响动频与动力响应、高转速下柔性结构动力刚化效应明显,微观结构尺度下的尺寸效应提高刚度并严重影响动力特性。更多还原

【Abstract】 Flexible bodies with different structure form are widely used in many industrial and technological systems, such as rotary machine, aerospace, vehicle engineering, mechanical arm and micro electro mechanical systems(MEMS). Construction members in these systems undergo large scale rigidity motion as well as elastic deformation. Inertial forces caused by the coupling between the rigid motion and elastic deformation play a key role to the dynamics characteristics for structures. Since that researches to the dynamics on the rigidity-flexible coupling are very important to dynamic analysis, system design and control of flexible multibody system(FMS). Theories on the motion and deformation coupling is a unification between the rigid-body dynamics and the deformable body mechanics. The dynamic formulations developed in this field must take account of the coupling effects between the rigid displacement and the deformation in deformable body, moreover, when ignoring the elastic deformation, the formulation can degenerate to the rigid-body dynamics, and when ignoring the rigid motion, the formulation can degenerate to the deformable body mechanics. There are several research topics which are of current interest, among these topics are the construction for dynamic formulation, computational strategies, impact and contact problem for the FMS and the fluid-structure interaction. Many problems are still not solved completely as a result of the nonlinearity in geometry, motion, Physics and material. Otherwise, the generalized elasticity has been developed deeply in recent years, few research has been given to the generalized elastic body undergoing large scale displacement.The dynamic problem on a single flexible body should firstly be solved, when to formulate the kinetic equation for the FMS. On the base of the research at home and abroad on both the flexible multibody system dynamics(FMD) and generalized elasticity, In this dissertation, we focus on the dynamic formulation for the generalized elastic body undergoing rigid rotating and its computational strategies. The generalized elasticity contains three material parameter is put forward, and the structure with different size scale were analyzed. The dynamic models are developed for the generalized elastic body in the centrifugal field with fixed rotational axis and various rotational speed, also the finite element formulation was derived. The classic rotating cantilever beam is simulated in centrifugal field with both the constant rotational speed and various rotational speed. The main works and conclusions in this dissertation are as follows:①The equations of linear and angular momentum conservation are derived for the generalized elasticity. basing on the couple stress elasticity theory and the micropolar theory. Combining the principle of virtual work with the theorem for the isotropic tensor, the modified relationship was put forward for the couple stress and the curvature tensor, moreover the kinetic equation and the boundary conditions were given for the generalized elastic body.②The finite element equation was formulated for the generalized elastic body, on the base of the method of weighted residuals and the constrained variational principle,with both the displacement and rotational angle considered as independent variables. The 4-nodes and 12-Dofs plane isoparametric element was constructed as well as the 8-nodes and 48-Dofs hexahedron isoparametric element for generalized elastic body. The analysis results to the simple shear problem and the cantilever with different size scale conclude that the generalized elasticity expands the classic elasticity to the micro size scale, and provides much more information than the classic elasticity and the beam theory in the structure analysis.③The dynamic model was developed for the double freedom vibration system, so as to investigate the effects of the centrifugal force, coriolis force and force caused by the eccentricity. For a two-Dofs springmass model, both the float frame reference and the fixed frame reference were introduced to described the motion of the mass point, applying the orthogonal tensor and the Rodriguez rotating formula, the velocity and the acceleration are given, and the dynamics formulation are derived for the fixed axis rotational springmass. The simulation results discovered that the centrifugal force and Coriolis force are play a key role to the dynamic characteristic as well as the eccentricity effect.④The dynamic formulation was constructed for a generalized elastic body rotating along a fixed axis, for the various speed conditions. In the float frame reference, the centrifugal force, Coriolis force and tangential inertial force was investigated. The equations of linear and angular momentum conservation are depicted based on the continuum mechanics analysis method as well as the boundary conditions.⑤The principle of virtual work was adopted to derived the finite element equation for the generalized elastic body in the centrifugal field. The finite element formulation for the classic elastic body undergoing large rigid rotation was also been deduced by the lagrange methods, and the dynamic stiffening effects because of the geometrical non-linearity was discussed in the initial stress methods. The 8-nodes and 48-Dofs hexahedron isoparametric element was extended to the finite element formulation in the motion-deformation coupling simulation for the generalized elastic body.⑥Simulations has been given to a typical cantilever beam rotating around a fixed axis with both the constant speed status and various speed status. Dynamic frequencies and responses for cantilever with different rotating configuration and size scale were evaluated. The results indicate that the dynamic frequencies and responses are different for the different rotating configuration, the dynamic stiffening effect become obviously for the flexible structure in the higher rotating speed conditions, and the size effects can’t be ignored when for the micro size structure.更多还原