Study On Scale Effect Of The Dynamic Characteristic Of Micro-beam

The micro electronic mechanical system(MEMS),famed for its superiority of miniaturization,high integration and high production levels,will become one of the domain industries for the future development.The analysis of micro-beam,which is one of the most common structure in MEMS,is the foundation for further development of MEMS.For lots of experiments proved that there exist obvious scale effect which analyzed through classic elasticity,it is the inevitable trend to establish an appropriate theoretical model for micro size structure.The first frequency of cantilever micro-beam which predicted by classical elasticity is far lower than which measured by experiments.Generalized elasticity is especially applicable to structure dynamics analysis with scale effect,where both the rotational deformation and couple stress is taken into account,also the measurement of deformation is improved.This paper establishes the finite element dynamic equations of generalized elasticity through the principle of virtue work,then use numerical analysis method to study the natural frequency and vibration mode of cantilever micro-beam and clamped-clamped micro-beam.The results show that the existent of scale effect of its natural frequency is related to its corresponding mode.The corresponding natural frequencies of bending and torsional modes have significant increment compared to classical elasticity,for the torsional mode is taken into consideration.However,little change of natural frequency of tensile mode can be observed for there is no rotational deformation.The scale effect of micro-beam’s natural frequency is also related to constraint where the scale effect of clamped-clamped micro-beam’s natural frequency is significantly lower than cantilever micro-beam’s,which means rotational deformation also affected by the size of restraining factor.The relation of stationary and moving state is a cosmopolitan science puzzle.For the rotational structures of MEMS always remain high speed rotation,it is of great significance to study whether the scale effect exist in the coupling of high speed rotation and deformation.This paper has established a generalized elastic dynamic model in centrifugal field based on generalized elasticity,then used the model to analyze the dynamic characteristic of fixed-axis rotating beam.The result showed that the natural frequencies of rotating beam changed when the rotate speed and attitude changed.There also exits significant scale effect of natural frequencies of rotating micro-beam,and it has the same variation trend with macro-size rotating beam.