Numerical and analytical approximations to large post-buckling deformation of MEMS

Zavracky, 1997, Micromechanical switches fabricated using nickel surface micromachining, J Microelectromech Syst, 6, 3, 10.1109/84.557524 Peroulis, 2002, Design of low actuation voltage RF MEMS switches, IEEE MTT-S Int Microwave Symp Digest, 165 Zhao J, Jia JY, Chen GY. A novel MEMS parallel-beam acceleration switch. In: Proceedings of the IEEE/ASME international conference on mechatronic and embedded systems and applications, Beijing, China; 2006. p. 349–53. Sharma, 2007, Fabrication and characterization of millimeter-size dielectric membranes prepared by RF sputtering and bulk micromachining techniques, Sensor Lett, 5, 552, 10.1166/sl.2007.230 Rhoads J, Shaw SW, Turner KL. Nonlinear dynamics and its applications in micro- and nanoresonators. In: Proceedings of the 2008 ASME dynamic systems and control conference, DSCC2008, 20–22 October, Ann Arbor, MI, USA; 2008. p. 2406. Hsu TR, Sun N. Residual stresses/strains analysis of MEMS. In: Proceedings of the international conference on modeling and simulation of microsystems, MSM1998 Santa Clara, CA; 1998. p. 82–7. Osterberg PM, Yie H, Cai X, White J, Senturia S. Self-consistent simulation and modeling of electrostatically deformed diaphragms. In: Proceedings of the IEEE MEMS 94, Oiso, France; 1994. p. 28–32. Osterberg PM. Electrostatically actuated microelectromechancial test structures for material property measurements. PhD dissertation. Massachusetts Institute of Technology; 1995. Gupta RK. Electrostatic pull-in test structure design for in-situ mechanical property measurements of microelectromechanical systems (MEMS). PhD dissertation. Massachusetts Institute of Technology; 1997. Nemirovsky, 2001, A methodology and model for the Pull-In parameters of electrostatic actuators, J Microelectromech Syst, 10, 601, 10.1109/84.967384 Kramer, 2002, Postbuckled micromachined square membranes under differential pressure, J Micromech Microeng, 12, 475, 10.1088/0960-1317/12/4/322 Denhoff, 2003, A measurement of Young's modulus and residual stress in MEMS bridges using a surface profiler, J Micromech Microeng, 13, 686, 10.1088/0960-1317/13/5/321 Krylov, 2008, The pull-in behavior of electrostatically actuated bistable microstructures, J Micromech Microeng, 18, 055026, 10.1088/0960-1317/18/5/055026 Najafi, 1989, A novel technique and structure for the measurement of intrinsic stress and Young's modulus of thin films, Proc IEEE Microelectromech Syst, 96 Osterberg, 1997, M-test: A test chip for MEMS material property measurement using electrostatically actuated test structures, J Microelectromech. Syst, 6, 107, 10.1109/84.585788 Seok, 2002, A new electrical residual stress characterization using bent beam actuators, J Micromech Microeng, 12, 562, 10.1088/0960-1317/12/5/308 Chen, 2002, Modification of curvature-based thin-film residual stress measurement for MEMS applications, J Micromech Microeng, 12, 917, 10.1088/0960-1317/12/6/324 Long DS, Shannon MA, Aluru NR. A novel approach for determining Pull-In voltages in micro-electro-mechanical systems (MEMS). In: Proceedings of the international conference on modeling and simulation of Microsystems, MSM2000 US Grant Hotel, San Diego, CA; 2000. p. 481–84. Ansola, 2007, A simple evolutionary topology optimization procedure for compliant mechanism design, Finite Elem Anal Des, 44, 53, 10.1016/j.finel.2007.09.002 Chu, 2007, A low actuation voltage electrostatic actuator for RF MEMS switch applications, J Micromech Microeng, 17, 1649, 10.1088/0960-1317/17/8/031 Fang, 1994, Post buckling of micromachined beams, J Micromech Microeng, 4, 116, 10.1088/0960-1317/4/3/004 Abu-Salih S, Elata D. Electromechanical buckling of a pre-stressed layer bonded to an elastic foundation. In: Proceedings of the international conference on modeling and simulation of Microsystems, MSM 2004 Boston, MA; 2004. p. 223–26. Elata, 2005, Analysis of a novel method for measuring residual stress in micro-systems, J Micromech Microeng, 15, 921, 10.1088/0960-1317/15/5/004 Rhoads, 2006, The nonlinear response of resonant microbeam systems with purely-parametric electrostatic actuation, J Micromech Microeng, 16, 890, 10.1088/0960-1317/16/5/003 Krylov, 2007, Lyapunov exponents as a criterion for the dynamic pull-in instability of electrostatically actuated microstructures, Int J Non-Linear Mech, 42, 626, 10.1016/j.ijnonlinmec.2007.01.004 Krylov, 2008, Parametric Excitation and Stabilization of Electrostatically Actuated Microstructures, Int J Multiscale Comput Eng, 6, 563, 10.1615/IntJMultCompEng.v6.i6.50 Mestrom, 2008, Modelling the dynamics of a MEMS resonator: simulations and experiments, Sensors Actuators A, 142, 306, 10.1016/j.sna.2007.04.025 Seydel, 1994 Wu, 2006, Improved harmonic balance approach to periodic solutions of non-linear jerk equations, Phys Lett A, 354, 95, 10.1016/j.physleta.2006.01.020 Wu, 2006, An analytical approximate technique for a class of strong non-linear oscillators, Int J Non-Linear Mech, 41, 766, 10.1016/j.ijnonlinmec.2006.01.006 Wu, 2007, Analytical approximations to large post-buckling deformation of elastic rings under uniform hydrostatic pressure, Int J Mech Sci, 49, 661, 10.1016/j.ijmecsci.2006.11.003 Yu, 2008, Analytical approximations to large hygrothermal buckling deformation of a beam, J Struct Eng ASCE, 134, 602, 10.1061/(ASCE)0733-9445(2008)134:4(602) Timoshenko, 1961 Thompson, 1973 Zhang, 2004, Numerical analysis of theoretical model of the RF MEMS switches, ACTA Mech Sin, 20, 178, 10.1007/BF02484263 Zhu, 2004, Effect of temperature on capacitive RF MEMS switch performance—a coupled-field analysis, J Micromech Microeng, 14, 1270, 10.1088/0960-1317/14/8/021