This work presents an investigation into the effect of nonlinearities on the response of a micro-electro-mechanical system gas sensor under mechanical shock and electrostatic loading. The gas sensor consists of a cantilever microbeam with a rigid microplate (micro-paddle) attached to its tip. A nonlinear Euler-Bernoulli beam theory is used to model the system, accounting for both geometric and inertia nonlinearities, in addition to the nonlinear electrostatic force used to actuate the system. The system of integro-partial-differential equations is discretized using a Galerkin procedure to extract a reduced-order model, which is then used for dynamic simulations of the system responses. The influences of the different components of nonlinearity such as geometric and inertia nonlinearities are examined. The results of the nonlinear model are compared to results obtained from linear beam theory and finite element simulations. For mechanical shock loading, both quasi-static and dynamic responses of a microbeam are considered. The effect of nonlinearity is found to be significant when the deflection of the microbeam exceeds around 30% of its length. The consequence of the large deflection is that the geometric nonlinearity has a much stronger influence on the response in comparison to the inertia nonlinearity. It is also apparent that the effect of the paddle is to enhance the dynamic, as opposed to the quasi-static, response of the microbeam to mechanical shock. For electrostatic actuation, it is found that using a nonlinear beam model to predict the pull-in and the deflection produces a slight improvement over using a linear beam model.
Abdel-RahmanEMYounisMIad NayfehAH (2002) Characterization of the mechanical behavior of an electrically actuated microbeam. Journal of Micromechanics and Microengineering12(6): 759–759.
2.
AboelkassemYNayfehAHGhommemM (2010) Bio-mass sensor using an electrostatically actuated microcantilever in a vacuum microchannel. Microsystem Technologies16(10): 1749–1755.
3.
AlsaleemFMYounisMI (2010) Stabilization of electrostatic MEMS resonators using a delayed feedback controller. Smart Materials and Structures19: 035016–035016.
4.
AlsaleemFMYounisMIIbrahimM (2009) A study for the effect of the PCB motion and electrostatic force on the dynamics of MEMS devices under mechanical shock. Journal of Microelectromechanical Systems18(3): 597–609.
5.
Arafat HN (1999) Nonlinear response of cantilever beams. PhD Dissertation, Virginia Tech, Blacksburg, VA.
6.
BaseltaDRFruhbergerBKlaassenaECemalovicSBrittonCLJrPatelSV (2003) Design and performance of a microcantilever-based hydrogen sensor. Sensors and Actuators B88: 120–131.
7.
BrownTGDavisBHepnerDFaustJMyersCMullerP (2001) Strap-down microelectromechanical (MEMS) sensors for high-g munition applications. IEEE Transactions in Magnetics37: 336–342.
8.
CurranoLJBaumanSChuramanWPeckerarMWienkeJKimS (2008) Latching ultra-low power mems shock sensors for acceleration monitoring. Sensors and Actuators A: Physical147(2): 490–497.
9.
CurranoLJYuMBalachandranB (2010) Latching in a MEMS shock sensor: modeling and experiments. Sensors and Actuators A: Physical159(1): 41–50.
10.
Fang XW, Huang QA and Tang TY (2004) Modeling of MEMS reliability in shock environments. In Proceedings of 7th International Conference on Solid-State and Integrated Circuits Technology, Beijing, China, 18–21 October 2004, vol. 2, pp. 860–863.
11.
FirdausSMOmarHAzidIA (2012) High sensitive piezoresistive cantilever MEMS based sensor by introducing stress concentration region (SCR). In: Ebrahimi (ed) Finite Element Analysis - New Trends and Developments, Croatia: InTech, pp. 225–252.
12.
FrobeniusWDZeitmanSAWhiteMHO’SullivanDDHamelRG (1972) Microminiature ganged threshold accelerometers compatible with integrated circuit technology. IEEE Transactions on Electron Devices19(1): 37–40.
13.
GhaffarianRSuttonDGChafeePMarquezNSharmaAKTeverovskiA (2002) Thermal and mechanical reliability of five COTS MEMS accelerometers. NASA Electronic Parts and Packaging Program. Technical Report, February 2002.
14.
Ghisi A, Kalicinski S, Mariani S, De Wolf I and Corigliano A (2008) Numerical-experimental comparison of low-g and high-g tests on a polysilicon MEMS accelerometer. In Proceedings of 9th International Conference on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, Freiburg, Germany, 21--23 April 2008.
15.
GhisiAKalicinskiSMarianiSDe WolfICoriglianoA (2009) Polysilicon MEMS accelerometers exposed to shocks: numerical–experimental investigation. Journal of Micromechanics and Microengineering19: 035023–035023.
16.
GoJSChoYHKwakBMParkK (1996) Snapping microswitches with adjustable acceleration threshold. Sensors and Actuators A: Physical54: 579–583.
17.
GuoZYYangZCLinLTZhaoQCDingHTLiuXS (2011) Design, fabrication and characterization of a latching acceleration switch with multi-contacts independent to the proof-mass. Sensors and Actuators A: Physical166(2): 187–192.
18.
Hamilton WR (1834) On a general method in dynamics. Philosophical Transaction of the Royal Society Part II pp. 247–308. [From the collection of Sir William Rowan Hamilton (1805–1865): Mathematical Papers edited by David R. Wilkins, School of Mathematics, Trinity College, Dublin, Ireland. (2000); also reviewed as On a General Method in Dynamics].
19.
Hamilton WR (1835) On a general method in dynamics. Philosophical Transaction of the Royal Society Part I pp. 95–144. [From the collection Sir William Rowan Hamilton (1805–1865): Mathematical Papers edited by David R. Wilkins, School of Mathematics, Trinity College, Dublin, Ireland. (2000); also reviewed as On a General Method in Dynamics].
20.
Hartzell A and Woodilla D (1999) Reliability methodology for prediction of micromachined accelerometer stiction. In Proceedings of IEEE International Reliability Physics Symposium, San Diego, California, USA, 23--25 March 1999, pp. 202–205.
21.
HazewinkelM (2001a) Runge-Kutta method. Encyclopedia of Mathematics, Berlin: Springer.
22.
HazewinkelM (2001b) Newton method. Encyclopedia of Mathematics, Berlin: Springer.
23.
ItôK (1993) Methods other than difference methods. In: ItoK (ed) Encyclopedic Dictionary of MathematicsVol. 2, 2nd edn. Cambridge, MA: MIT Press, pp. 1139–1980.
24.
JiaMLiXSongZBaoMWangYYangH (2007) Micro-cantilever shocking-acceleration switches with threshold adjusting and ‘on’-state latching functions. Journal of Micromechanics and Microengineering17: 567–575.
25.
Kazinczi R, Mollinger JR, and Bossche A (2001) Environment induced failure modes of thin film resonator. J Microlit Microfab Microsyst 1: 63--69.
26.
KrylovSMaimonR (2004) Pull-in dynamics of an elastic beam actuated by continuously distributed electrostatic force. Journal of Vibration and Acoustics126: 332–342.
27.
Kurth S, Shaporin A, Hiller K, Kaufmann Ch and Gessner T (2008) Reliability of MEMS devices in shock and vibration overload situations. In Proceedings of SPIE vol. 6884, pp. 688409.
28.
LokeYMcKinnonGHBrettMJ (1991) Fabrication and characterization of silicon micromachined threshold accelerometers. Sensors and Actuators A: Physical29(3): 235–240.
29.
McNamaraSGianchandaniYB (2004) Liga fabricated 19-element threshold accelerometer array. Sensors and Actuators A: Physical112(1): 175–183.
30.
Man PF and Mastrangelo CH (1994) Surface micromachined shock sensor for impact detection. In Proceedings of Solid-State Sensor and Actuator Workshop, Hilton Head Island, South Carolina, USA, 13--16 June 1994, pp. 156–159.
31.
MatsunagaTEsashiM (2002) Acceleration switch with extended holding time using squeeze film effect for side airbag systems. Sensors and Actuators A: Physical100(1): 10–17.
32.
NayfehAHBalachandranB (1995) Applied Nonlinear Dynamics, New York: Wiley.
33.
NayfehAHOuakadHMNajarFChouraSAbdel-RahmanEM (2009) Nonlinear dynamics of a resonant gas sensor. Nonlinear Dynamics59(4): 607–618.
34.
NoetzelJTnnesenTBeneckeWBinderJMaderG (1996) Quasianalog accelerometer using microswitch array. Sensors and Actuators A: Physical54: 574–578.
35.
Nouira H, Foltête E, Hirsinger L and Ballandras S (2007) Mechanical shock as a source for energy harvesting using MEMS. In Proceedings of IMAC-XXV: Conference & Exposition on Structural Dynamics, Orlando, FL, 19--22 February 2007.
36.
Ouakad HM and Younis MI (2008) Modelling and simulation of a cantilever-paddle beam under the effect of capillary, shock, and electrostatic forces. In Proceedings of the ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Brooklyn, NY, 3--6 August 2008.
37.
OuakadHMYounisMI (2011) Natural frequencies and mode shapes of initially curved carbon nanotube resonators under electric excitation. Journal of Sound and Vibration330: 3182–3195.
38.
OuakadHMYounisMIAlSaleemFM (2012) Dynamic response of an electrostatically actuated microbeam to drop-table test. Journal of Micromechanics and Microengineering22: 095003–095003.
39.
Pustan M, Belcin O and Golinval JC (2011) Dynamic investigations of paddle MEMS cantilevers used in mass sensing applications. In Proceedings of 3rd International Conference on Advanced Engineering in Mechanical Systems, Cluj-Napoca, Romania, 21--23 September 2011.
40.
Robinson C, Overman D, Warner R and Blomqulst T (1987) Problem encountered in the development of the microscale g-switch using three design approaches. In Proceedings of Digest, 6th International Conference on Solid-State Sensors and Actuators (Transducers ’87), Tokyo, Japan, 2--5 June 1987, pp. 410–413.
41.
SelvakumarA (2001) A wide-range micromachined threshold accelerometer array and interface circuit. Journal of Micromechanics and Microengineering11(2): 118–125.
42.
SheehyMPunchJGoyalSReidMLishchynskaMKellyG (2009) The failure mechanisms of micro-scale cantilevers under shock and vibration stimuli. Strain45: 283–294.
43.
ShinKPyoSLeeYS (2009) Simple feed-forward active control method for suppressing the shock response of a flexible cantilever beam. Smart Materials and Structures18: 027001–027001.
44.
SundaramSTormenMTimotijevicBLockhartROverstolzTStanleyRP (2011) Vibration and shock reliability of MEMS: modeling and experimental validation. Journal of Micromechanics and Microengineering21: 045022–045022.
45.
TimoshenkoS (1953) History of Strength of Materials, New York: McGraw-Hill.
46.
TongCJLinMT (2009) Design and development of a novel paddle test structure for the mechanical behavior measurement of thin films application for MEMS. Microsystem Technologies15(8): 1207–1216.
47.
TonnesenTLudtkeONoetzelJBinderJMaderG (1997) Simulation, design and fabrication of electroplated acceleration switches. Journal of Micromechanics and Microengineering7: 237–239.
48.
VahdatASRezazadehGAfrangS (2011) Improving response of a MEMS capacitive microphone filtering shock noise. Microelectronics Journal42: 614–621.
49.
Walter PL (2008) How high in frequency are accelerometer measurements meaningful. PCB Peizoelectronics, Technical Note # TN25. www.pcb.com (accessed 15 June 2013)..
50.
WangJLiX (2010) A high-performance dual-cantilever high-shock accelerometer single-sided micromachined in (111) silicon wafers. Journal of Microelectromechanical Systems19(6): 1515–1520.
51.
WangYHLeeCYChiangCM (2007) A MEMS-based air flow sensor with a free-standing micro-cantilever structure. Sensors7(10): 2389–2401.
52.
WellsRL (2001) Using shock response spectra to design motion control profiles for flexible structures. Journal of Vibration and Control7: 905–921.
53.
WyciskMTonnesenTBinderJMichaelisSTimmeHJ (2000) Low-cost post-CMOS integration of electroplated microstructures for inertial sensing. Sensors and Actuators A: Physical83: 93–100.
54.
Yang C, Zhang B, Chen B and Lin L (2010) Drop-shock dynamic analysis of MEMS/Package system. In Proceedings of IEEE 23rd International Conference on Micro Electro Mechanical Systems (MEMS), Wanchai, Hong Kong, 24--28 Janruary 2010.
55.
YapFFHarmokoHLiuMVahdatiN (2007) Modeling of hard disk drives for shock and vibration analysis – consideration of nonlinearities and discontinuities. Nonlinear Dynamics50: 717–773.
56.
Yee JK, Yang HH and Judy JW (2002) Dynamic response and shock resistance of ferromagnetic micromechanical magnetometers. In Proceedings of Fifteenth IEEE International Conference on Micro Electro Mechanical Systems, Las Vegas, NV, 24--24 Janruary 2002.
57.
YounisMIJordyDPitarresiJ (2007) Computationally efficient approaches to characterize the dynamic response of microstructures under mechanical shock. Journal of Microelectromechanical Systems16: 628–638.
58.
YueMLinHDedrickDESatyanarayanaSMajumdarABedekarAS (2004) A 2-D microcantilever array for multiplexed biomolecular analysis. Journal of Microelectromechanical Systems13(2): 290–299.
