guided beam
TRANSCRIPT
Microsystems LaboratoryUC-Berkeley, ME Dept.
Parametric and Optimal Design of MEMS – Class#9MEMS Class#9
Liwei Lin
Professor, Dept. of Mechanical Engineering
Co-Director, Berkeley Sensor and Actuator Center
1Liwei Lin, University of California at Berkeley
The University of California, Berkeley, CA94720
e-mail: [email protected]
http://www.me.berkeley.edu/~lwlin
Microsystems LaboratoryUC-Berkeley, ME Dept.
Outline
General Solving Procedures for Meandering Flexures
Nonlinear Effects of Beams to Systems
Sensor Designs
2Liwei Lin, University of California at Berkeley
Meandering Flexure
3
Examples
4
Solving Processes
Continue on x & y components
5
Free-Body Diagram
6/12/00 6
Unified Beam Bending Theory
Continue withBeam2, 3 … 7
6/12/00 7
Summary
8
Matrix to Solve M0 (set 7 = 0)
9
Continue: Solution Procedures
Please read Professor Pisano’s class notes for detail derivations.In principle, the 51 unknowns can be solved.The values of , x, y on each b b l l d
10
beam can be calculated.
One can derive kx & ky
Example: ky
11
Example: Boundary Conditions
12
Example: Fixed-Guided Beam
13
Example: Fixed-Guided Beam
14
Non-linear Behavior
15
Sources of Nonlinearity
16
Estimation of Shear Effects
17
Width & Thickness Convention
18
Beam Curvature
19
MEMS Spring Hardening Effect
20
MEMS Spring Hardening Effect
21
Detailed Derivations in theOld lecture notes
MSMS Beams – short summary
22
MSMS Beam Examples
23
6/12/00 24
Duffing Equation
25
Duffing Equation
26
Percentage Nonlinearity
27
Resonant Sensor Designs
28
Capacitive Gyro Sensors
• Simplified Gyro Structure
Sense
Drive
Sense electrode
Drive electrode
Gyro Design
• Drive modeF iFrequency is about 9900Hz
Gyro Design
• Sense modeF iFrequency is
about 10016Hz