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。
A generalized linear elastic model is proposed with the couple-stress elastic theory.The strain and curvature tensor of the elastic body is described in kinematics by translational and rotational deformations,corresponding to the internal force stress and couple-stress respectively.For the case of the rigid body rotation with known rotational speed,the kinematics-deformation coupling kinetic model of the couple-stress elastic body is derived by using Hamilton′s principle.Moreover,the relative inertia force,centrifugal force,Coriolis inertia force and tangential inertia force are taken into account in this model.The finite element equations of the couple-stress elastic body is established using the constrained variation principle by using the hexahedron solid isoparametric element with 8nodes and 48degrees-of-freedom and taking the displacement and the deformation angle as independent variables.A cantilever beam rotating about a fixed axis is used here as an application example to explore the dynamic characteristics and the dynamic response.The first mode characteristic of the rotational rectangular beam goes to two cases with different constant rigid rotational velocities,one of which decreases to vanish and the other remains the same with the rotational speed increasing.The displacement,deformation rotor angle,and the dynamic stress and couple stress of the rotational beam versus time are numerically implemented while the rigid body rotates with variable speed.The dynamics analysis research for the fixed-axis rotation structure can provide theoretical model and numerical analysis method.
出处
《振动工程学报》
EI
CSCD
北大核心
2016年第1期50-60,共11页
Journal of Vibration Engineering
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)
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
couple-stress elastic theory
rigid-flexible coupling
kinematics-deformation coupling model
effect of inertia force
constrained variation principle
