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Thermal vibration and nonlinear buckling of micro-plates under partial excitation
European Journal of Mechanics - A/Solids ( IF 4.1 ) Pub Date : 2020-12-05 , DOI: 10.1016/j.euromechsol.2020.104185
Arash Kazemi , Ramin Vatankhah

In this study, a finite element formulation is proposed to study bending, thermal vibration, and buckling behavior of a modified couple stress-based micro-plate under partial piezoelectric excitation. To this end, the micro-plate is modeled using the classical plate theory (CPT) in conjunction with von Kármán nonlinear strains. The modified couple stress theory is employed to take into account the size-dependent behavior of the system. The nonlinear equations of motion are derived using Hamilton's principle. In order to obtain numerical solutions to the problem, the displacement finite element model is developed. A parameter study is conducted to study the effects of different parameters, such as temperature rise, material length parameter scale (MLSP), boundary conditions, aspect ratio, and piezoelectric layers configurations on nonlinear behavior of micro-plates. The results are divided into three separate sections: static bending analysis, thermal vibration analysis, and thermal buckling analysis; in each section, the accuracy of the model is checked by comparing the results with the ones reported in the literature. Obtained results show that the bending behavior of the micro-plate is influenced by the size effects and piezoelectric configurations; furthermore, it is observed that applied voltage to the piezoelectric layers and temperature rise affect the fundamental frequency of the system. Finally, the effect of piezoelectric layers on the buckling behavior of the model is studied; the results show that the fully covered model is less prone to buckling under the thermal loading cases. The proposed model provides good control over the mechanical performance of plate-like components, which makes the model widely applicable in the design and optimization of Micro-Electro-Mechanical-Systems (MEMS).



中文翻译:

部分激励下微板的热振动和非线性屈曲

在这项研究中,提出了一种有限元公式来研究部分压电激励下基于耦合应力的微板的弯曲,热振动和屈曲行为。为此,使用经典板理论(CPT)结合vonKármán非线性应变对微板进行建模。采用改进的耦合应力理论来考虑系统的尺寸依赖性行为。非线性运动方程是根据汉密尔顿原理导出的。为了获得该问题的数值解,建立了位移有限元模型。进行参数研究以研究不同参数的影响,例如温度上升,材料长度参数尺度(MLSP),边界条件,长宽比,和压电层配置对微板非线性行为的影响。结果分为三个独立的部分:静态弯曲分析,热振动分析和热屈曲分析。在每个部分中,通过将结果与文献报道的结果进行比较来检查模型的准确性。结果表明,微板的弯曲行为受尺寸效应和压电结构的影响。此外,观察到施加到压电层的电压和温度升高影响系统的基频。最后,研究了压电层对模型屈曲行为的影响。结果表明,在热负荷情况下,完全覆盖的模型不太容易屈曲。

更新日期:2020-12-29
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