EE 245: Introduction to MEMSLecture 16: Beam CombosCTN 10/20/091Copyright © 2009 Regents of the University of CaliforniaFolded-Beam Stiffness Ratios• In the x-direction:•In the zdirection:Folded-beam suspension324LEIkzx=In the z-direction:ª Same flexure and boundary conditions• In the y-direction:Shuttle324LEIkxz=EWh8EE C245: Introduction to MEMS Design LecM 8 C. Nguyen 9/28/07 31• Thus: AnchorFolding trussLEWhky8=24⎟⎠⎞⎜⎝⎛=WLkkxyMuch stiffer in y-direction![See Senturia, §9.2]Folded-Beam Suspensions Permeate MEMSGyroscope [Draper Labs.]Accelerometer [ADXL-05, Analog Devices]EE C245: Introduction to MEMS Design LecM 8 C. Nguyen 9/28/07 32Micromechanical Filter [K. Wang, Univ. of Michigan]Folded-Beam Suspensions Permeate MEMS• Below: Micro-Oven Controlled Folded-Beam ResonatorEE C245: Introduction to MEMS Design LecM 8 C. Nguyen 9/28/07 33Stressed Folded-FlexuresEE C245: Introduction to MEMS Design LecM 8 C. Nguyen 9/28/07 34EE 245: Introduction to MEMSLecture 16: Beam CombosCTN 10/20/092Copyright © 2009 Regents of the University of CaliforniaClamped-Guided Beam Under Axial Load• Important case for MEMS suspensions, since the thin films comprising them are often under residual stress• Consider small deflection case: y(x) « LxzG vernin differential equati n: (Euler Beam Equati n)LWxyEE C245: Introduction to MEMS Design LecM 8 C. Nguyen 9/28/07 35Governing differential equation: (Euler Beam Equation)Unit impulse @ x=LAxial LoadDesign Implications• Straight flexuresª Large tensile S means flexure behaves like a tensioned wire (for which k-1= L/S)ª Large compressive S can lead to buckling (k-1→ ∞)gp g()• Folded flexuresª Residual stress only partially releasedª Length from truss to shuttle’s centerline differs EE C245: Introduction to MEMS Design LecM 8 C. Nguyen 9/28/07 40centerline differs by Lsfor inner and outer
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