悬臂微梁固有频率和模态的尺寸效应

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (12) : 187-192.

论文

悬臂微梁固有频率和模态的尺寸效应

谢新吉1,刘占芳1,2,3,杜丘美1

作者信息 +

Scale effect on the natural frequency and vibration mode of a cantilever micro beam

XIE Xinji1,LIU Zhanfang1，2，3,DU Qiumei2

Author information +

文章历史 +

摘要

采用经典弹性力学预测悬臂微梁的基频远低于测量的结果，广义弹性力学由于计及了连续的旋转变形及相应的偶应力，完善了变形的度量，适用于分析结构动力学特性的尺寸效应。从虚功原理出发建立了广义弹性体的有限元动力学方程，对悬臂微梁的固有频率和模态进行了数值分析。结果表明，微梁的固有频率是否存在尺寸效应与对应的模态有关。微梁的弯曲和扭转模态由于包含了旋转变形，对应的固有频率较之经典弹性力学有显著提高，而拉压模态不涉及旋转变形，其固有频率没有明显变化。

Abstract

The first frequency of a cantilever microbeam predicted by classical elasticity is far lower than 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. The measurement of deformation was improved. Finite element dynamic equations of generalized elasticity were established through the principle of virtue work, and a numerical analysis method was used to study the natural frequency and vibration mode of the cantilever 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. The torsional mode is taken into consideration. However, little change of natural frequency of tensile mode can be observed because deformation is not involved.

导出引用

谢新吉1,刘占芳1,2,3,杜丘美1. 悬臂微梁固有频率和模态的尺寸效应[J]. 振动与冲击, 2018, 37(12): 187-192

XIE Xinji1,LIU Zhanfang1，2，3,DU Qiumei2. Scale effect on the natural frequency and vibration mode of a cantilever micro beam[J]. Journal of Vibration and Shock, 2018, 37(12): 187-192

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