中文摘要：

由于微尺度领域材料的力学性能存在尺度效应,使得微梁的动力学性态较传统的大尺寸柔性梁的动力学性态呈现明显的不同。对中心转动刚体、柔性微梁组成的刚体—微梁一类刚柔耦合系统的动力学特性进行研究。在柔性微梁变形位移中,计及横向位移引起轴向缩短的耦合变形量,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,由Hamilton原理推导出系统考虑尺度效应的刚柔耦合动力学方程。在此基础上,分析微梁固有频率对微尺度的依赖性,比较在不同转速下零次近似模型和一次近似模型振动频率的差异,从而确定在考虑尺度效应的微尺度下零次近似模型的适用范围,最后分析尺度效应和耦合变形量对微梁刚度的影响。研究表明,尺度效应提高微梁的固有频率,尺度效应对微梁刚度的影响是静态的,耦合变形量对微梁的刚度的影响与转速有关。

英文摘要：

The dynamic properties of the micro-beam are obviously different from those of the traditional macro-beam due to the size effect of material on a micro scale. The dynamics of a rigid-flexible coupling system consisting of a rotating hub and a flexible micro-beam also known as hub-microbeam system, is studied. The coupling terms of the deformation motion, caused by transverse displacement are taken into account in the deformation displacements of micro-beam. The dynamic characteristic of a micro beam is analyzed theoretically by using couple stress theory （Cosserat theory）. The governing equations of motion with the ＂dynamic stiffening＂ term and the size effect term for this system are derived by using the Hamilton principle. Based on the obtained dynamic equations, the dependence of the resonant frequency of a micro beam on its size is analyzed. For different rotating speeds, the vibration frequency of the zero order approximate model is compared with that of the coupling model and the suitable range of the zero order approximate model is determined, considering size effect on a micro scale. Finally, the influence of size effect and coupling terms of the deformation motion on the stiffness of micro beam is analyzed. The simulation demonstrates that the resonant frequency of micro-beam increases because of size effect. The influence of size effect is static and that of coupling terms of the deformation motion is related to the rotating speed.