变截面耦合微悬臂双梁的基本振动特性
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摘要
本文研究了连接部件的几何参数对变截面耦合微悬臂双梁振动特性的影响.首先,利用集总参数法建立了等效的两自由度系统耦合振动的解析模型;其次,利用分离变量法获得了耦合双梁自由振动的固有频率、振幅比和强迫振动的反共振频率;最后,通过比对解析解、有限元数值结果和实验数据,验证了解析预测的可靠性.研究结果表明,连接部件的宽度和初始偏转角的变化会对耦合双梁振动的特性产生较大的影响.
The paper focuses on the study of the influence of the geometric parameters of the connection component on the vibration characteristics of a coupled double-microcantilever beam with a variable cross-section. First, the analytical model for an effective coupled two-degree-freedom system is established by the lumped parameter method. Second, the natural frequency, the amplitude ratio of the free vibration and the anti-resonance frequency of forced vibration of the coupled double-beam are obtained by the separation variable method. Finally, the reliability of the present analytical prediction is verified by comparing the analytical solution with finite element numerical results and the experimental data. Theoretical analyses show that the width and deflection angle of the connector have a great influence on the vibration characteristics of the coupled double-microcantilever beam.
The paper focuses on the study of the influence of the geometric parameters of the connection component on the vibration characteristics of a coupled double-microcantilever beam with a variable cross-section. First, the analytical model for an effective coupled two-degree-freedom system is established by the lumped parameter method. Second, the natural frequency, the amplitude ratio of the free vibration and the anti-resonance frequency of forced vibration of the coupled double-beam are obtained by the separation variable method. Finally, the reliability of the present analytical prediction is verified by comparing the analytical solution with finite element numerical results and the experimental data. Theoretical analyses show that the width and deflection angle of the connector have a great influence on the vibration characteristics of the coupled double-microcantilever beam.
引文
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[3]LI M,TANG H X,ROUKES M L.Ultra-sensitive NEMS-based cantilevers for sensing,scanned probe and very high-frequency applications[J].Nature Nanotechnology,2006,2(2):114-120.
[4]TAMAYO J,KOSAKA P M,RUZ J J,et al.Biosensors based on nanomechanical systems[J].Chemical Society Reviews,2013,42(3):1287-1311.
[5]ALVAREZ M,LECHUGA L M.Microcantilever-based platforms as biosensing tools[J].The Analyst,2010,135(5):827-836.
[6]WANG D F,KEISUKE C,TSUYOSHI I,et al.Mode localization analysis and characterization in a5-beam array of coupled nearly identical micromechanical resonators for ultra-sensitive mass detection and analyte identification[J].Microsystem Technologies,2012,18(11):1923-1929.
[7]SPLETZER M,RAMAN A,WU A Q,et al.Ultrasensitive mass sensing using mode location in coupled microcantilevers[J].Applied Physics Letters,2006,88(25):254102.
[8]SPLETZER M,RAMAN A,SUMALI H,et al.Highly sensitive mass detection and identification using vibration localization in coupled microcantilever arrays[J].Applied Physics Letters,2008,92(11):11402.
[9]ZHANG H M,HUANG J,YUAN W Z,et al.An acceleration sensing method based on the mode localization of weakly coupled resonators[J].Journal of Microelectromechanical Systems,2016,25(2):286-296.
[10]ZHANG H M,HUANG J,YUAN W Z,et al.A high-Sensitivity micromechanical electrometer based on mode localization of two degree-of-freedom weakly coupled resonators[J].Journal of Microelectromechanical Systems,2016,25(5):937-946.
[11]WANG D F,XU D,WANG T,et al.Multiplication in frequencies by synchronized and superharmonic oscillations:sensing verification with picogram order microspheres[J].IEEE Sensors Journal,2015,15(8):4464-4471.
[12]WANG D F,XU D,WANG X,et al.Improving pictogram mass sensitivity via frequency doubling in coupled silicon micro-cantilevers[J].Journal of Micromechanics and Microengineering,2016,26(1):015006.
[13]KENIG E,CROSS M C,LIFSHITZ R,et al.Passive phase noise cancellation scheme[J].Physical Review Letters,2012,108(26):264102.
[14]MORSHED S,PROROK B C.Tailoring beam mechanics towards enhancing detection of hazardous biological species[J].Experimental Mechanics,2007,47(3):405-415.
[15]王大甲,胡放荣,姚军,等.基于微悬臂梁的化学传感器的灵敏度研究[J].传感技术学报,2008,21(8):1333-1336.
[16]JEONG B,CHO H,KEUM H,et al.Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane[J].Nanotechnology,2014,25(46):465-501.
[17]陈金龙,吴君正,张能辉.开孔变截面微悬臂梁传感器的等效刚度和固有频率[J].传感技术学报,2017,30(9):1324-1329.
[18]魏星,陈莘莘,童谷生,等.基于自然单元法的功能梯度板固有频率优化[J].力学季刊,2017,38(1):135-143.
[19]刘扭扭,张振果,徐时吟,等.基于动力反共振结构的周期细直梁纵向局域共振带隙研究[J].振动与冲击,2017,36(24):143-147.
[20]JEONG B,CHO H,YU M F,et al.Nonlinear hardening and softening resonances in micromechanical cantilever-nanotube systems originated from nanoscale geometric nonlinearities[J].International Journal of Solids and Structures,2012,49(15):2059-2065.