微型Mindlin板非线性动力学模型的建立
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国家自然科学基金资助项目(11472019)


Nonlinear dynamics model of the micro-Mindlin plate based on the strain gradient theory
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    摘要:

    随着MEMS技术工艺的发展,微型结构在工程领域的应用越来越广泛.对于微型结构,经典连续介质力学理论的本构关系中不包含任何特征长度尺度,不能反映结构在微米尺度下的尺寸效应.本文基于Von Karman大变形理论和一阶剪切变形理论,把考虑尺寸效应的应变梯度理论推广至微型Mindlin板的非线性问题.分别计算微结构的应变能,包括宏观变形应变能和微观变形应变能两部分,结合微型Mindlin板结构的动能及外力功,代入Hamilton原理,得到了微型Mindlin板在大变形情况下的非线性动力学方程及边界条件.

    Abstract:

    With the development of MEMS fabricating technology, MEMS structure now has a wide application in manufacturing industry. Meanwhile, because of no any characteristic length scale parameters in constitutive relationship, the classical theory of continuum mechanics is unlikely to predict the size effect under micro scale. This paper investigates the nonlinear problems of micro Mindlin plates based on the firstorder shear deformation theory and von Karman nonlinearity, and the strain gradient theory is also utilized to take size effect into consideration. Nonlinear dynamic model of the micro Mindlin plate along with its boundary conditions are obtained by taking strain energy, including strain energy of both macro and micro deformation, kinetic energy and external work into Hamilton′s principle.

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赵猛,陈丽华,张伟.微型Mindlin板非线性动力学模型的建立[J].动力学与控制学报,2016,14(3):205~210; Zhao Meng, Chen Lihua, Zhang Wei. Nonlinear dynamics model of the micro-Mindlin plate based on the strain gradient theory[J]. Journal of Dynamics and Control,2016,14(3):205-210.

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历史
  • 收稿日期:2015-06-09
  • 最后修改日期:2015-08-09
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  • 在线发布日期: 2016-05-26
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