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基于广义弹性理论的微梁固有频率及模态的尺寸效应

沈暗明 陈锐 杜丘美

沈暗明, 陈锐, 杜丘美. 基于广义弹性理论的微梁固有频率及模态的尺寸效应[J]. 应用数学和力学, 2018, 39(9): 999-1008. doi: 10.21656/1000-0887.380301
引用本文: 沈暗明, 陈锐, 杜丘美. 基于广义弹性理论的微梁固有频率及模态的尺寸效应[J]. 应用数学和力学, 2018, 39(9): 999-1008. doi: 10.21656/1000-0887.380301
SHEN Anming, CHEN Rui, DU Qiumei. Scale Effects on Natural Frequencies and Vibration Modes of Micro Cantilever Beams Based on Generalized Elasticity[J]. Applied Mathematics and Mechanics, 2018, 39(9): 999-1008. doi: 10.21656/1000-0887.380301
Citation: SHEN Anming, CHEN Rui, DU Qiumei. Scale Effects on Natural Frequencies and Vibration Modes of Micro Cantilever Beams Based on Generalized Elasticity[J]. Applied Mathematics and Mechanics, 2018, 39(9): 999-1008. doi: 10.21656/1000-0887.380301

基于广义弹性理论的微梁固有频率及模态的尺寸效应

doi: 10.21656/1000-0887.380301
基金项目: 国家自然科学基金(51505044)
详细信息
    作者简介:

    沈暗明(1991—),男,硕士(通讯作者. E-mail: sam@cqu.edu.cn).

  • 中图分类号: O343

Scale Effects on Natural Frequencies and Vibration Modes of Micro Cantilever Beams Based on Generalized Elasticity

Funds: The National Natural Science Foundation of China(51505044)
  • 摘要: 经典弹性理论在近代工程技术中得到广泛应用,但其本构关系中不包含任何与尺寸相关的参数,因此不适用于微观结构,不能预测和解释尺寸效应.广义弹性理论增加了偶应力及其对应的曲率张量,完善了对小变形的几何描述,适用于微结构的尺寸效应研究.该文采用广义弹性理论,并结合Hamilton变分原理推导了悬臂微梁的振动微分方程,对微梁的固有频率及其模态进行了分析.结果表明,随着微梁厚度的不断减小,固有频率的尺寸效应与其对应的模态密切相关.扭转和弯曲模态包含了旋转变形,其对应的固有频率显著提高,表现出了显著的尺寸效应;而拉压模态不涉及旋转变形,固有频率未产生明显变化,没有尺寸效应.
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出版历程
  • 收稿日期:  2017-12-05
  • 修回日期:  2018-01-09
  • 刊出日期:  2018-09-15

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