Topics covered and supplementary notes
| Week | Dates Topics | Notes/References | Assignments |
| 1 |
Aug. 5:
The structure of micromechanical elements: why is it the way it is?
Aug. 7: Slender elements in micro/nano mechanical elements Essential concepts in mechanics: exemplification to an axially loaded bar. Start of the slender beam theory |
Read Glimpses of MEMS History for a quick
overview of microsystems and microfabrication.
A pioneering paper by Roylance and Angell Chapter 4 in MaSS book . |
Homework #1 |
| 2 |
Aug. 12:
Beam theory and solving problems with it. Analyzing micromechanical suspensions. Aug. 14: Static indterminacy and resolving it. Energy methods in mechanics. |
Chapter 4 in MaSS book Steps in deformation analysis of beams |
Homework #2 |
| 3 |
Aug. 19:
Multi-axial stiffness analysis of compliant suspensions using beam finite element code
Aug. 21: Multi-axial stffness analysis (contd.): resolving static indeterminacy |
Chapter 4 in MaSS book .
Steps in deformation analysis of beams Beam finite element code in Matlab Analysis of pin-wheel suspension |
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| 4 |
Aug. 26:
Strain energy in axial and bending modes of deformation; Castigliano's theorems; Maxwell's
reciprocity theorem; Betti-Maxwell theorem
Aug. 28: Illustration of the use of Castigliano's theorems State of stress in a beam; shear stress concept; Poisson effect and the derivation of the shear modulus; Derivation of the static equilibrium equations of elastic continuum in 2D. |
Chapter 4 in MaSS book . Proof of Castigliano's theorems Derivation of the governing differential equations of an elastic continuum |
Homework #3 |
| 5 |
Sep. 2:
State of stress in a beam subjected bending and shear; reconciliation of the beam theory with the continuum theory;
comparison of strain energies associated with bending, shear, and axial modes of deformation
Sep. 4: Coordinate transformation of stress, strain, and inertia tensors; Mohr's circle; concept of tensors; torsion, shear and twist. |
Chapter 4 in MaSS book . |
- |
| 6 |
Sep. 9:
Residual stress, thermal stress, and heterogeneous layered beams
Sep. 11: Residual stress gradient and ensuing curling; helical beams; concept of buckling |
Chapter 4 in MaSS book . |
- |
| 7 |
Sep. 16:
Midterm examination
(open book, open notes for 90 min from 8:30 am to 10:00 am in the class room)
Sep. 18: Electrostatics and its coupling with mechanics using a beam actuated with a pair of charges; stability analysis using force-balance method; pull-in concept. |
Chapter 6 in MaSS book . |
- |
| 8 |
Sep. 23:
Equations of electrostatics.
Sep. 25: Discritization of coupled electrostatic-elastostatic equations; compuation using beam finite elemenet codes. |
Chapter 6 in MaSS book . 3D FEA beam code |
Homework #4 |
| 9 |
Sep. 30:
Energy approach to understand the electrostaic and elastostatic equations
Oct. 2: Maxwell stress tensor and body force; solving coupled equations |
Chapter 6 in MaSS book . Coupled electrostatic-elastostatic code using beam elements |
- |
| 10 |
Oct. 7:
Equations of electrostatics and their coupling with equations of elasto-statics; Energy method; static and dynamic pull-in voltages. Oct. 9: Dynamic pull-in voltage; energy landscape ofelectromechanics. |
Chapter 6 in MaSS book . 2D Electrostatic analysis code in Matlab with GUI Pull-in analysis code with GUI. |
Re-submission of hand-written midterm solutions by Oct. 14. 2014. |
| 11 |
Oct. 14:
Dynamics of electrostatically actuated micromechanical structures Oct. 16: Lumped modeling of inertia (mass) Squeezed film effects and lumped modeling |
Chapter 6 in MaSS book . Coupled electrostatic-elastostatic dynamic analysis code using beam elements |
Homework #5 One-page project proposal |
| 12 |
Oct. 21:
Computing effective mass of slender beams Couette flow and dmaping on translating plates Suqeeze film effects on micromechanical structures Oct. 23: HAPPY (Holiday; no class) |
Chapter 6 in MaSS book . Slides on squeeze-film effects |
- |
| 13 |
Oct. 28:
Circuit model for squeeze-film damping; electrothermal actuators.
Oct. 30: Electro-thermal-elastic coupled analysis; free and forced vibrations; magnetic actuation Oct. 31: Self-heated piezoresistor problem |
Chapter 6 in MaSS book . Free and forced vibrations of a 1-dof system Electro-thermal microactuators Coupled electromechanics FEA for solving the electrostatics problem Simple notes for understanding finite element method for linear elastic problems Self-heated piezoresistor problem |
Homework #6 |
| 14 |
Nov. 4:
Happy Moharram!(Holiday, no class)
Nov. 6: Happy Gurunanak Jayanthi! (Holiday, no class again) Nov. 7: Tutorial class converted to lecture class from 5:30 pm to 6:50 pm Magnetic microactuators |
Chapter 6 in MaSS book . |
- |
| 15 |
Nov. 11:
Magnetic actuators (contd.) Circuit modeling: effort and flow variables; generalized resistor, capacitor, inductor, gyrator, and transformer; two-port elements Nov. 13: Piezoresistive effect and its coupeld modeling | - | - |
| 16 |
Nov. 18:
Piezoeresistive effect modeling (contd.) Piezoelectric equations Nov. 20: Scaling effects in MEMS | Scaling MEMS | - |
| 17 | Nov. 20: Thermoelastic damping-a quick overview of the phenomenon and equations | - | - |
| 18 |
Nov. 29:
Project presentations from 9 am to 1 pm and then 2 pm to 3:30 pm
Dec. 3: Final examination: 2 to 5 pm in TF-10 in thr CeNSE building |
See details on project presentations and supplementary files
Final exam of 2010 Final exam of 2011 (Comsol software-based) |
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