基于修正耦合应力理论的旋转多晶硅微板动力学建模及非线性振动

IF 4.2 2区 工程技术 Q1 MECHANICS
Guiqin He , Zhi Li , Haichao Gui , Dengqing Cao
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引用次数: 0

摘要

针对微机电系统的核心元件——旋转悬臂多晶硅微板,提出了一种新的动态建模方法。详细研究了旋转矩形悬臂微板的自振特性和复杂的非线性动力响应。考虑侧向变形产生的非线性耦合变形项,采用修正的耦合应力理论确定了系统的应变能和动能。利用拉格朗日方程和切比雪夫多项式导出了系统的离散控制方程。通过对旋转矩形悬臂微板的动力响应和模态特性的收敛和对比研究,验证了该方法的准确性和有效性。最后,通过数值分析研究了尺寸相关、无因次旋转角速度和纵横比对动态特性的影响。结果表明,考虑尺寸效应时,微孔板的刚度会发生变化,导致固有频率增大,而动力响应减小。此外,本文还讨论了转速和展弦比对动态特性的复杂影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Dynamic modeling and nonlinear vibrations of a rotating poly-crystalline silicon microplate based on the modified couple stress theory
A novel dynamic modeling method is proposed for a rotating cantilever poly-crystalline silicon microplate which is the core element of the micro-electro-mechanical system in this work. The natural vibration characteristics and complicated nonlinear dynamic responses of the rotating rectangular cantilever microplate are investigated in detail. Considering the nonlinear coupling deformation terms derived from the lateral deformation, the strain energy and kinetic energy of the system are determined by using the modified couple stress theory. The discrete governing equations of the system are derived by employing the Lagrange equations and the Chebyshev polynomials. The accuracy and validity of the present method for the rotating rectangular cantilever microplate are demonstrated by the convergence and comparison studies of the dynamic response and modal characteristics. Finally, the effects of the size-dependency, dimensionless rotational angular velocity and aspect ratio on dynamic properties are investigated through numerical analysis. It is shown that the stiffness of the microplate will change when the size effects are considered, which results in an increase of natural frequency but a decrease of dynamic responses accordingly. Besides, the complex influences of the rotating velocity and the aspect ratio on the dynamic characteristics are discussed in the present work.
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来源期刊
CiteScore
7.00
自引率
7.30%
发文量
275
审稿时长
48 days
期刊介绍: The European Journal of Mechanics endash; A/Solids continues to publish articles in English in all areas of Solid Mechanics from the physical and mathematical basis to materials engineering, technological applications and methods of modern computational mechanics, both pure and applied research.
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