弹性体作定轴转动的耦合动力学模型与数值分析

发布时间：2018-02-04 01:02

本文关键词： 偶应力弹性理论刚-柔耦合运动与变形耦合模型惯性力效应约束变分原理　出处：《振动工程学报》2016年01期 　论文类型：期刊论文

【摘要】：应用含偶应力的弹性理论建立弹性力学模型,应变和曲率张量分别描述弹性体的平动变形和旋转变形,且分别对应于应力和偶应力两种内力。对已知定轴变转速刚体转动的情况,采用哈密尔顿原理建立了含偶应力弹性体作定轴刚体转动的运动与变形耦合动力学模型,模型计及了相对惯性力、离心力、科氏力和切向惯性力。考虑以弹性体的位移和变形转角为独立变量,利用约束变分原理建立了含偶应力弹性体作定轴刚体转动的有限元方程,其中单元离散采用8个节点48个自由度的三维六面体实体等参元。以绕定轴旋转的悬臂梁为例,数值分析了旋转悬臂梁的动力学特性和动力学响应。当幅值变化但刚体转速恒定时,旋转方梁的一阶特征频率出现随转速增加保持不变和下降两种情况。当刚体变转速时,考察了旋转悬臂梁位移、变形转角、动态应力以及偶应力的时变规律。该研究可为作定轴旋转系统的结构部件的动力学分析提供理论模型和数值分析方法。
[Abstract]:The elastic mechanics model is established by using the elastic theory with couple stress. The strain and curvature Zhang Liang describe the translational deformation and the rotational deformation of the elastomer, respectively. And corresponding to two kinds of internal forces, stress and couple stress, the rotation of rigid body with constant axis and variable rotation speed is known. The coupling dynamic model of motion and deformation of elastic body with couple stress is established by using Hamilton principle. The relative inertia force and centrifugal force are taken into account in the model. Considering the displacement and deformation angle of elastic body as independent variables, the finite element equation of rigid body rotation with couple stress is established by using constrained variational principle. The element discretization uses eight nodes 48 degrees of freedom three-dimensional hexahedron entity isoparametric element. Take the cantilever beam rotating around the fixed axis as an example. The dynamic characteristics and dynamic response of the rotating cantilever beam are numerically analyzed. When the amplitude changes but the rotation speed of the rigid body is constant. The first order characteristic frequency of the rotating square beam is invariant and decreasing with the increase of the rotational speed. When the rigid body changes the rotational speed, the displacement and the deformation angle of the rotating cantilever beam are investigated. This study can provide a theoretical model and a numerical analysis method for the dynamic analysis of the structural components of a fixed axis rotation system.
【作者单位】：重庆大学煤矿灾害动力学与控制国家重点实验室;重庆大学航空航天学院;中国工程物理研究院总体工程研究所;
【基金】：国家自然科学基金面上项目资助(11372365) 国家自然科学基金委员会和中国工程物理研究院联合基金资助项目(11176035)
【分类号】：O343
【正文快照】： 引言刚柔耦合系统的动力学分析在航空航天、机器人和高速旋转机构等领域具有重要的理论和工程应用价值。譬如直升机旋翼、卫星天线、太阳能帆板和大型涡轮机叶片等,这类系统的运动变量既有大范围的刚体转动,又有小幅度的弹性变形,二者产生运动学耦合。国内外许多学者[1-16]对

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