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 #4
Assigned: Sep. 23rd, 2014
Due: Sep. 30th, 2014
Points: 100

  1. 80 points
    Twelve micromechanical suspension designs are shown in Suspensions2014.pdf file. The same 12 are also shown below against a square grid. Each grid-square is 5 microns by 5 microns. Assume that the thickness is uniformly 2 microns and the in-plane width of the beams is also 5 microns. Assume that the suspensions are made of polysilicon with Young's modulus equal to 155 GPa and density 2300 kg/m3.

    Choose a suspension based on your birth-month. If you were born in January, choose (a), February (b), and so on.
    Using 3D beam FEM code , compute translational and rotations stiffness of the central mass along and about all three axes.
    If an acceleration of 1 g acts on the mass in all three directions, by how much does it move in different directions? What is the maximum principal stress in each case? Consider each case separately first and then together.
  2. 20 points
    A cantilever beam of 200 microns length, 20 microns in-plane width, and 5 microns thick is suspended over a substarte with 2 micorns gap. At the free end of the cantilever there is a charge Q and right below it on the substarte there is 1 femto-Coulomb charge exists. Write a Matlab program to find Q at which pull-in occurs. Draw the displacement vs. Q curve and also plot the "energy landscape".

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