基于广义弹性理论的微梁固有频率及模态的尺寸效应

Abstract

Classical elasticity has been widely applied in engineering technologies. But the length scale parameter is not included in the classical elasticity, which leads to the scale effects on mechanical characteristics and no longer satisfies the micro scale. Generalized elasticity is especially applicable to microstructures with scale effects, where both the rotational deformation and the couple stress are taken into account, and the measurement of deformation is improved. By means of Hamilton’s variation principle and generalized elasticity, the vibration differential equations for the micro cantilever beam in different motion states were derived. Then natural frequencies and vibration modes of the micro cantilever beam were analyzed. The results show that, with the decreasing of the micro beam height, the scale effect on the natural frequency is closely related to the mode. The corresponding natural frequencies of torsional and bending modes have significant increment and scale effect compared with those according to the classical elasticity, for the rotational deformation is considered. However, little variation of the natural frequency of the tensile mode is found because there is no rotational deformation involved.