Mechanical Engineering, Indian Institute of
Science, Bangalore 560 012, India
Think big abut small things.
ME 237 and NE 211
Mechanics of Microsystems : Micro/nano Mechanics
Aug.-Dec., 2014
Instructor: G. K.
Ananthasuresh, Room 106, ME Building, suresh at
mecheng.iisc.ernet.in
Homework #5
Assigned: Oct. 16th, 2014
Due: Oct. 23rd, 2014
Points: 90
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30 points
Shown in the figure below is a parallel-plate model of an electromechnaical microactuator.
(a) Derive the static equilibrium equation using the energy method.
(b) Derive the static and dynamic pull-in voltages in symbolic form
(c) For what value of Cs does the stable range of static equilibrium solution extends through the entire gap?
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30 points
Shown in the figure below is a fixed-fixed slender nano-mechanical beam and located very close to it a short fixed electrode.
While the two ends of the long beam are fixed, the bottom of the electrode is fixed. There is a small gap underneath the beam,
which enables it deform. The beam and the fixed electrode are made of silicon nitride and gold layers. Orange layer on top is the
gold layer.
If the beam's dimensions are 40,000 nm x 200 nm x (100+75) nm, those of the short fixed electrode are 10,000 nm x 2000 nm
x (100+75) nm, and the lateral gap between the beam and the electrode is 165 nm, find the pull-in voltage. Note that the
thickness of silicon nitride is 100 nm and that of gold is 75 nm.
Use analytical modeling and beam finite element modeling. Take the following properties: Young's modulus of silicon nitride is 310 GPa
and its dielectric constant is 6. Young's modulus of gold is 79 GPa.
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30 points
Shown in the figure below is a two degree-of-freedom model of a electromechanical bandpass filter.
(a) Write the equations of equilibrium for this model.
(b) Find all equilibrum solutions for the following data: k1 = 2 N/m;
j2 = 3 N/m; kc = 0.2 N/m; g10 = 2 um; g20 = 1 um; A1 = 4E-10 m^2; A2 = 6E-10 m^2; phi1 = 0.25 V; and phi2 = 0.15 V.
(c) Compute the pull-in voltages when one voltage is fixed at a value while the other is varied.
(d) Plot the energy landscape and submit the code for extra 30 points .