多段微梁固有振动特性的尺寸效应分析

Size effect analysis of natural vibration characteristics of multi-segment micro-beam

尺寸效应将影响多段微梁的固有振动特性。针对微机电系统中一种三段式微梁,基于哈密顿原理建立了多段微梁的无阻尼自由振动方程,并求出微梁的固有频率和模态,将不同角度下的理论结果与有限元仿真进行对比验证。采用修正偶应力理论推导考虑材料尺度参数的多段微梁变形能表达式,并进行多段微梁固有频率和模态的尺寸效应分析。结果表明:随着材料尺度参数与特征尺寸比值的增大,多段微梁的固有频率逐渐增加。微梁各段间的角度越大,尺寸效应对1阶固有频率的影响越显著,而尺寸效应对微梁的模态几乎没有影响。

Size effect could affect the natural vibration characteristics of a multi-segment micro-beam. Aiming at a three-segment micro-beam in the micro-electro-mechanical system, the undamped free vibration equation of the multi-segment micro-beam is established based on the Hamilton principle. The natural frequency and mode of the micro-beam are calculated, and the results are compared with theoretical results by using finite element under different angles. The modified couple stress theory is used to derive the expression of the deformation energy of the multi-segment micro-beam considering the material-length-scale parameter, and the size effect of the natural frequency and mode of the multi-segment micro-beam are analyzed. The results show that with the increase of the ratio of the material-length-scale parameter to the characteristic size, the natural frequency of the multi-segment micro-beam gradually increases. The larger the angle between the segments of the micro-beam, the more significant the influence of the size effect on the 1st natural frequency, while the size effect has almost no influence on the mode of the multi-segment micro-beam.