离心场中含旋转梯度影响的弹性体动力特性分析

摘要：以含偶应力的弹性理论为基础，考虑小变形状态下弹性体的平动变形与旋转梯度，推导并给出了离心环境中一般弹性体运动与变形耦合动力学方程，以转角为独立变量，利用罚方法得到方程组的约束变分形式，构造了8结点48自由度的实体等参元，建立了离心场中含旋转梯度的一般弹性体动力特性分析的有限元模型。对绕中轴线旋转的悬臂梁进行动力特性分析，频率随转速的关系表明离心力和科氏力降低了该梁的一阶频率，但科氏力导致了二阶频率的上升，旋转梯度效应提高了弹性体的静力刚度，导致各阶频率出现刚化效应。

Dynamic analysis of elasitc body with rotation gradient effects in centrifugal field

The flexible body in a centrifugal field was analyzed dynamically,considering the rotation gradient effects.Based on the couple-stress theory,the kinetic equations were derived.A hexahedron solid isoparametric element was constructed,with the rotating angle as an independent variable,and the finite element model was established using the constrained variation principle.Dynamic characteristics of a cantilever beam revolving around the neutral axis were investigated.The relations between the natural frequencies and rotating speed were exploed,which describe that centrifugal and coriolis forces lead the first natural frequency to decrease,however the coriolis force results in the increase of second natural frequency.The stiffness of the flexible body is increased,as a result of the rotation gradient effects in microstructure field,and the resonant frequency is raised,comparing with the classic elasticity results.