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 #6
Assigned: Oct. 28th, 2014
Due: Nov. 4th, 2014
Points: 80
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30 points
A shallow V-shaped beam with theta degree angle at the corner of V is clamped at both the ends. The sides of the V are of L microns long.
The cross-section has area A and moment of inertia I. Young's modulus and coefficienct of thermal expansion are Y and alpha. If this beam is
uniformly heated to raise its temperature by T, what is the displacement at the corner of V?
Extra credit of 30 points if you do this problem for applied potential of phi between the two end of the V beam; take
electrical and themral conductivities to be ke and kth.
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30 points
Compute the time to close the gap of a spring-restrained parallel-plate capacitor with gap g0 and dielectric layer of thickness td
without and with squeeze-film effect when the applied volatge is 10% larger than the pull-in voltage. Take A = 200 microns by 10 microns,
gap g0 = 1 micron; td/epsilon_r = 0.2 microns; spring constant = k = 25 N/m; and ambient pressure = 1 bar.
Extra credit of 30 points for deriving the formulae and verifying with suitably modified Matlab code oneDdyn.m.
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20 points
Now that your project problem is fixed, please write the statement of your problem, scope of the problem, and specific equations you will
solve or complete details of the device you will simulate. In other words, show some progress in your thinking about the project problem.
It should be not more than two A4 size sheets. Half a page is also fine if you convey the details properly.