关键词: 尺度效应, 刚柔耦合系统, 固有频率, 耦合变形量, 微梁

Abstract: 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.

Key words: Micro-beam, Resonant frequency, Rigid-flexible coupling system, Size effect, The coupling terms of the deformation motion