CAJ | 학술논문

不少微观实验已经证实,微尺度领域材料的力学性能存在尺度效应.文章以转动刚体、柔性微梁组成的刚柔耦合系统为研究对象,采用偶应力理论(又称 Cosserat理论)研究微梁动力学特性的尺度效应,运用拉格朗日方程推导出系统考虑尺度效应的一次近似刚柔耦合动力学方程.仿真结果表明,较该文提出的一次近似耦合模型,传统的零次近似耦合模型在刚体作高速旋转时不能正确地描述微梁的动力学行为;尺度效应使微梁振动的振幅减小,频率增大.
불소미관실험이경증실,미척도영역재료적역학성능존재척도효응.문장이전동강체、유성미량조성적강유우합계통위연구대상,채용우응력이론(우칭 Cosserat이론)연구미량동역학특성적척도효응,운용랍격랑일방정추도출계통고필척도효응적일차근사강유우합동역학방정.방진결과표명,교해문제출적일차근사우합모형,전통적령차근사우합모형재강체작고속선전시불능정학지묘술미량적동역학행위;척도효응사미량진동적진폭감소,빈솔증대.
Many micro experiments have shown that the mechanical properties of materials at micro scale are size dependent. The dynamics of a rigid-flexible coupling system consisting of a rotating hub and a flexible micro beam is investigated in this paper. The dynamic characteristic of a micro beam is analyzed theoretically using couple stress theory (Cosserat theory). The governing equations of motion with the dynamic stiffening terms (referred as the first-order approximation coupling model) and the size effect term for this system are derived from Lagrange's equations. Compared with the model proposed in this paper,the traditional zero-order approximation model can not describe the dynamics of micro beam correctly when the hub is in high rotation speed. The size effect results in the descending of vibration amplitude and the increasing of vibration frequency of the micro beam.