考虑卡西米尔力的微纳镜扭转弯曲耦合模型
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摘要
为了研究卡西米尔力对静电驱动微纳镜的影响,文章建立了考虑卡西米尔力的微纳镜扭转弯曲耦合模型的归一化参数方程.通过数值解分析了归一化参数之间的关系,并与纯扭转模型进行对比.结果表明:忽略悬臂梁的弯曲变形,会导致微纳镜的吸合参数的值比实际值大,造成较大的误差;卡西米尔力的存在能够明显的减小微纳镜的归一化吸合角、归一化吸合电压和归一化吸合垂直位移;卡西米尔力对微纳镜归一化吸合参数的影响还与卡西米尔力影响因子有关,影响因子越大对吸合参数的影响越明显;若驱动电压为零,卡西米尔力的存在可能会导致微纳镜发生吸合.研究方法和结论为扭转微纳镜的设计和应用提供指导.
In order to study the influences of Casimir force on the micro-nano-mirror driven by electrostatic force, equations with normalized parameters of bending coupling model is established.The relationship between normalized parameters is analyzed through numerical solution, which is compared with the pure torsional model.The results show that neglecting the bending effect of the torsion beams in the pure torsional model makes value of normalized pull-in parameters of micro-nano-mirror larger.The existence of the Casimir force can significantly reduce the pull-in angle, pull-in voltage and pull-in deflection of micro-nano-mirror.And the effect of Casimir force on the micro-nano-mirror is related to the normalized influence factor of Casimir force.The influence on the pull-in parameters will be more obvious when the influence factor is bigger.When the driving voltage is zero, the presence of Casimir force may lead to the micro-nano-mirror pull-in.The method and conclusions provide guidance for the design and application of micro-nano-mirror.
In order to study the influences of Casimir force on the micro-nano-mirror driven by electrostatic force, equations with normalized parameters of bending coupling model is established.The relationship between normalized parameters is analyzed through numerical solution, which is compared with the pure torsional model.The results show that neglecting the bending effect of the torsion beams in the pure torsional model makes value of normalized pull-in parameters of micro-nano-mirror larger.The existence of the Casimir force can significantly reduce the pull-in angle, pull-in voltage and pull-in deflection of micro-nano-mirror.And the effect of Casimir force on the micro-nano-mirror is related to the normalized influence factor of Casimir force.The influence on the pull-in parameters will be more obvious when the influence factor is bigger.When the driving voltage is zero, the presence of Casimir force may lead to the micro-nano-mirror pull-in.The method and conclusions provide guidance for the design and application of micro-nano-mirror.
引文
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[12]Moeenfard H,Ahmadian M T.Analytical modeling of static behavior of electrostatically actuated nano/micromirrors considering van der Waals forces[J].Acta Mechanica Sinica,2012,28:729-736.
[13]Moeenfard H,Darvishian A,Ahmadian M T.A coupled bending torsion for electrostatically actuated torsional nano/microactuators with considering influence of van der Waals force[J].Acta Mechanica,2013,224:1791-1800.
[14]梁斌斌,张龙,王炳雷,等.考虑卡西米尔力的静电激励NEMS吸合特性及其尺寸效应研究[J].固体力学学报,2016,37(3):247-253.
[2]郭兴军,李朋伟,张文栋,等.基于电容式MEMS器件的静电斥力驱动研究[J].仪器仪表学报,2014,35(8):1738-1743.
[3]Ofir D,Eran S,Ariel L,et al.Pull-in study of an electrostatic torsion microactuator[J].Journal of Microelectromechanical Systems,1998,7(4):373-379.
[4]赵建平,陈花玲,陈玲莉,等.微镜扭转弯曲耦合变形静态特性分析[J].西安交通大学学报,2003,37(11):1179-1181.
[5]Huang J M,Liu A Q,Deng Z L,et al.An approach to the coupling effect between torsion and bending for electrostatic torsional micromirrors[J].Sensors and Actuators A,2004,115:159-167.
[6]王振霖,陈学康,曹生珠.大角度扭转微镜的静态特性分析[J].科学技术与工程,2008,8(16):1671-1819.
[7]罗伟,杨国珂,叶坤涛.串联电容对MEMS扭转微镜吸合角的影响[J].仪表技术与传感器,2014(4):98-101.
[8]Zhou S A.On forces in microelectromechanical systems[J].International Journal of Engineering Science,2003,41:313-335.
[9]Gusso A,Delben G J.Influence of the Casimir force on the pull-in parameters of silicon based electrostatic torsional actuators[J].Sensors&Actuators A Physical,2007,135(2):792-800.
[10]Vakili-Tahami F,Mobki H,Keyvani-Janbahan A,et al.Pull-in phenomena and dynamic response of a capacitive Nano-beam switch[J].sensors&transducers Journal,2009,110:26-37.
[11]Moeenfard H,Darvishian A,Ahmadian M T.Static behavior of nano/micromirrors under the effect of Casimirforce,an analytical approach[J].Journal of Mechanical Science and Technology,2011,26(2):537-543.
[12]Moeenfard H,Ahmadian M T.Analytical modeling of static behavior of electrostatically actuated nano/micromirrors considering van der Waals forces[J].Acta Mechanica Sinica,2012,28:729-736.
[13]Moeenfard H,Darvishian A,Ahmadian M T.A coupled bending torsion for electrostatically actuated torsional nano/microactuators with considering influence of van der Waals force[J].Acta Mechanica,2013,224:1791-1800.
[14]梁斌斌,张龙,王炳雷,等.考虑卡西米尔力的静电激励NEMS吸合特性及其尺寸效应研究[J].固体力学学报,2016,37(3):247-253.