柔性双稳态结构分岔跳跃模式的探讨
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摘要
针对柔性双稳态结构跳跃路径不唯一及其力位移曲线存在不连续点(即尖点)的问题,基于有限元大变形理论建立了双稳态柔性结构的跳跃控制方程,采用多步位移载荷循环加载/卸载的方法数值模拟了跳跃过程中存在的可能屈曲模态及其变换方式,得到了其对称跳跃分岔的完整解。分析了双稳态结构参数对跳跃不连续点(尖点)和跳跃路径的影响关系,提出将结构品质因数作为双稳态跳跃"尖点"判据的方法,得到了具有稳定单一跳跃路径的双稳态结构。采用热成型方法研制了类余弦梁双稳态结构,考虑残余应力、夹持边界条件及载荷加载方式的影响,仿真预测的屈曲模态转换过程与实验结果基本一致,为双稳态跳跃特征的精确设计与控制提供理论依据。
The discontinuity of the force-displacement curve(also named sharp point) and multiple snap-through pathways significantly affect the engineering practicability of compliant bistable structures. Hence, the snap-through controlling equation for compliant bistable structures is established according to the large deflection finite element theory. By using the multistep displacement loading method, the possible buckling modes and their transforming procedure are numerically obtained, which interprets reasonably the discontinuity of the force curve. Furthermore, the influence of the structure parameters on the sharp point and snap-through pathway is numerically analyzed, and meanwhile, the structural quality factor is introduced to judge the occurrence of the sharp point. Finally, the bistability design method for achieving stable bistable mechanics with single snapping pathway is proposed. For further validation, a thermal formed bistable beam structure with quasi-cosine shape is manufactured,and the simulated mode transforming process is nearly consistent with that from experiments considering the influences of residual stress, clamping status and loading conditions, thus providing a theoretical basis to design and control the bistable snapping characteristics of compliant structures.
The discontinuity of the force-displacement curve(also named sharp point) and multiple snap-through pathways significantly affect the engineering practicability of compliant bistable structures. Hence, the snap-through controlling equation for compliant bistable structures is established according to the large deflection finite element theory. By using the multistep displacement loading method, the possible buckling modes and their transforming procedure are numerically obtained, which interprets reasonably the discontinuity of the force curve. Furthermore, the influence of the structure parameters on the sharp point and snap-through pathway is numerically analyzed, and meanwhile, the structural quality factor is introduced to judge the occurrence of the sharp point. Finally, the bistability design method for achieving stable bistable mechanics with single snapping pathway is proposed. For further validation, a thermal formed bistable beam structure with quasi-cosine shape is manufactured,and the simulated mode transforming process is nearly consistent with that from experiments considering the influences of residual stress, clamping status and loading conditions, thus providing a theoretical basis to design and control the bistable snapping characteristics of compliant structures.
引文
[1]赵剑,陈国玺,高仁璟,等.基于磁-机耦合效应的大行程多稳态机构非线性跳跃分析[J].机械工程学报,2014,50(20):188-194.ZHAO Jian,CHEN Guoxi,GAO Renjing,et al.Nonlinear snap-through analysis of magnetic mechanical based large stroke multistable mechanism[J].Journal of Mechanical Engineering,2014,50(20):188-194.
[2]WU Yibo,DING Guifu,ZHANG Congchun,et al.Design and implementation of a bistable microcantilever actuator for magnetostatic latching relay[J].Microelectronics Journal,2010,41(6):325-330.
[3]LUHARUKA R,HESKETH P.Bistable electromagnetically actuated rotary gate microvalve[J].Journal of Micromechanics and Microengineering,2008,18(3):035015.
[4]SNELLER A,CETTE P,MANN B.Experimental investigation of a post-buckled piezoelectric beam with an attached central mass used to harvest energy[J].Proceedings of the Institution of Mechanical Engineers,Part I:Journal of Systems and Control Engineering,2011,225(4):497-509.
[5]HARNE R,WANG K W.A review of the recent research on vibration energy harvesting via bistable systems[J].Smart Materials and Structures,2013,22(2):023001.
[6]HANSEN B,CARRON C,JENSEN B,et al.Plastic latching accelerometer based on bistable compliant mechanisms[J].Smart Materials and Structures,2007,16(5):1967-1972.
[7]赵剑,魏岩,高仁璟,等.基于局部截面构型优化的双稳态结构跳跃阈值控制与设计[J].机械工程学报,2016,52(19):154-161.ZHAO Jian,WEI Yan,GAO Renjing,et al.Control of the snap-through characteristic through local cross-section optimization[J].Journal of Mechanical Engineering,2016,52(19):154-161.
[8]QIU Jin,LANG J,SLOCUM A.A curved-beam bistable mechanism[J].Journal of Microelectromechanical systems,2004,13(2):137-146.
[9]ZHAO Jian,JIA Jianyuan,HE Xiaoping,et al.Post-buckling and snap-through behavior of inclined slender beams[J].Journal of Applied Mechanics,2008,75(4):041020.
[10]HUANG Yu,ZHAO Jian,LIU Shutian.Design optimization of segment-reinforced bistable mechanisms exhibiting adjustable snapping behavior[J].Sensors and Actuators A:Physical,2016,252:7-15.
[11]ZHANG Aimei,CHEN Guimin.A comprehensive elliptic integral solution to the large deflection problems of thin beams in compliant mechanisms[J].Journal of Mechanisms and Robtics,2013,5(2):021006.
[12]CHEN Guimin,GOU Yanjie,ZHANG Aimei.Synthesis of compliant multistable mechanisms through use of a single bistable mechanism[J].Journal of Mechanical Design,2011,133(8):081007.
[13]勾燕洁,张守银,陈贵敏.一种全柔顺六稳态机构的设计[J].机械工程学报,2015,51(7):61-66.GOU Yanjie,ZHANG Shouyin,CHEN Guimin.Design approach for a fully compliant sexastable mechanism[J].Journal of Mechanical Engineering,2015,51(7):61-66.
[14]CAZOTTES P,FERNANDES A,POUGET J,et al.Bistable buckled beam:Modeling of actuating force and experimental validations[J].Journal of Mechanical Design,2009,131(10):101001.
[15]PHAM Huytuan,WANG Dungan.A quadristable compliant mechanism with a bistable structure embedded in a surrounding beam structure[J].Sensors and Actuators A:Physical,2011,167(2):438-448.
[16]KRYLOV S,ILIC B,LULINSKY S.Bistability of curved microbeams actuated by fringing electrostatic fields[J].Nonlinear Dynamics,2011,66(3):403-426.
[17]HUSSEIN H,LE MOAL P,BOURBON G,et al.Modeling and stress analysis of a pre-shaped curved beam:influence of high modes of buckling[J].International Journal of Applied Mechanics,2015,7(04):1550055.
[18]ZOU Hongxiang,ZHANG Wenming,WEI Kexiang,et al.A compressive-mode wideband vibration energy harvester using a combination of bistable and flextensional mechanisms[J].Journal of Applied Mechanics,2016,83(12):121005.
[19]HUANG Henwei,LEE Fuwei,YANG Yaojoe.Design criteria for a push-on push-off MEMS bistable device[J].Journal of Microelectromechanical Systems,2016,25(5):900-908.
[20]HAO Guangbo,MULLINS J.On the comprehensive static characteristic analysis of a translational bistable mechanism[J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2016,230(20):3803-3817.
[21]CAMESCASSE B,FERNANDES A,POUGET J.Bistable buckled beam:Elastica modeling and analysis of static actuationp[J].International Journal of Solids and Structures,2013,50(19):2881-2893.
[22]CAMESCASSE B,FERNANDES A,POUGET J.Bistable buckled beam and force actuation:Experimental validations[J].International Journal of Solids and Structures,2014,51(9):1750-1757.
[23]王勖成.有限单元法[D].北京:清华大学出版社,2003.WANG Xucheng.Finite element method[D].Beijing:Tsinghua University Press,2003.
[2]WU Yibo,DING Guifu,ZHANG Congchun,et al.Design and implementation of a bistable microcantilever actuator for magnetostatic latching relay[J].Microelectronics Journal,2010,41(6):325-330.
[3]LUHARUKA R,HESKETH P.Bistable electromagnetically actuated rotary gate microvalve[J].Journal of Micromechanics and Microengineering,2008,18(3):035015.
[4]SNELLER A,CETTE P,MANN B.Experimental investigation of a post-buckled piezoelectric beam with an attached central mass used to harvest energy[J].Proceedings of the Institution of Mechanical Engineers,Part I:Journal of Systems and Control Engineering,2011,225(4):497-509.
[5]HARNE R,WANG K W.A review of the recent research on vibration energy harvesting via bistable systems[J].Smart Materials and Structures,2013,22(2):023001.
[6]HANSEN B,CARRON C,JENSEN B,et al.Plastic latching accelerometer based on bistable compliant mechanisms[J].Smart Materials and Structures,2007,16(5):1967-1972.
[7]赵剑,魏岩,高仁璟,等.基于局部截面构型优化的双稳态结构跳跃阈值控制与设计[J].机械工程学报,2016,52(19):154-161.ZHAO Jian,WEI Yan,GAO Renjing,et al.Control of the snap-through characteristic through local cross-section optimization[J].Journal of Mechanical Engineering,2016,52(19):154-161.
[8]QIU Jin,LANG J,SLOCUM A.A curved-beam bistable mechanism[J].Journal of Microelectromechanical systems,2004,13(2):137-146.
[9]ZHAO Jian,JIA Jianyuan,HE Xiaoping,et al.Post-buckling and snap-through behavior of inclined slender beams[J].Journal of Applied Mechanics,2008,75(4):041020.
[10]HUANG Yu,ZHAO Jian,LIU Shutian.Design optimization of segment-reinforced bistable mechanisms exhibiting adjustable snapping behavior[J].Sensors and Actuators A:Physical,2016,252:7-15.
[11]ZHANG Aimei,CHEN Guimin.A comprehensive elliptic integral solution to the large deflection problems of thin beams in compliant mechanisms[J].Journal of Mechanisms and Robtics,2013,5(2):021006.
[12]CHEN Guimin,GOU Yanjie,ZHANG Aimei.Synthesis of compliant multistable mechanisms through use of a single bistable mechanism[J].Journal of Mechanical Design,2011,133(8):081007.
[13]勾燕洁,张守银,陈贵敏.一种全柔顺六稳态机构的设计[J].机械工程学报,2015,51(7):61-66.GOU Yanjie,ZHANG Shouyin,CHEN Guimin.Design approach for a fully compliant sexastable mechanism[J].Journal of Mechanical Engineering,2015,51(7):61-66.
[14]CAZOTTES P,FERNANDES A,POUGET J,et al.Bistable buckled beam:Modeling of actuating force and experimental validations[J].Journal of Mechanical Design,2009,131(10):101001.
[15]PHAM Huytuan,WANG Dungan.A quadristable compliant mechanism with a bistable structure embedded in a surrounding beam structure[J].Sensors and Actuators A:Physical,2011,167(2):438-448.
[16]KRYLOV S,ILIC B,LULINSKY S.Bistability of curved microbeams actuated by fringing electrostatic fields[J].Nonlinear Dynamics,2011,66(3):403-426.
[17]HUSSEIN H,LE MOAL P,BOURBON G,et al.Modeling and stress analysis of a pre-shaped curved beam:influence of high modes of buckling[J].International Journal of Applied Mechanics,2015,7(04):1550055.
[18]ZOU Hongxiang,ZHANG Wenming,WEI Kexiang,et al.A compressive-mode wideband vibration energy harvester using a combination of bistable and flextensional mechanisms[J].Journal of Applied Mechanics,2016,83(12):121005.
[19]HUANG Henwei,LEE Fuwei,YANG Yaojoe.Design criteria for a push-on push-off MEMS bistable device[J].Journal of Microelectromechanical Systems,2016,25(5):900-908.
[20]HAO Guangbo,MULLINS J.On the comprehensive static characteristic analysis of a translational bistable mechanism[J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2016,230(20):3803-3817.
[21]CAMESCASSE B,FERNANDES A,POUGET J.Bistable buckled beam:Elastica modeling and analysis of static actuationp[J].International Journal of Solids and Structures,2013,50(19):2881-2893.
[22]CAMESCASSE B,FERNANDES A,POUGET J.Bistable buckled beam and force actuation:Experimental validations[J].International Journal of Solids and Structures,2014,51(9):1750-1757.
[23]王勖成.有限单元法[D].北京:清华大学出版社,2003.WANG Xucheng.Finite element method[D].Beijing:Tsinghua University Press,2003.