bistable conditions

28
Bistable conditions • It turns out that if the beam is made initially curved without prestress, there’ll be conditions for the beam to be bistable. • The following cosine shape is mathematically proved to be conditionally bistable and its f- d curve is mathematically calculated.

Upload: gotzon

Post on 21-Jan-2016

57 views

Category:

Documents


1 download

DESCRIPTION

Bistable conditions. It turns out that if the beam is made initially curved without prestress, there’ll be conditions for the beam to be bistable. The following cosine shape is mathematically proved to be conditionally bistable and its f-d curve is mathematically calculated. - PowerPoint PPT Presentation

TRANSCRIPT

Page 1: Bistable conditions

Bistable conditions

• It turns out that if the beam is made initially curved without prestress, there’ll be conditions for the beam to be bistable.

• The following cosine shape is mathematically proved to be conditionally bistable and its f-d curve is mathematically calculated.

Page 2: Bistable conditions

• In Jeffery Lang’s paper, there is a parameter defined as Q=h/t, where h is the apex height, and t is the thickness of the beam.

• In the paper, it is proved that if Q<2.31, the beam cannot be bistable.

• Another requirement for being bistable is that the 2nd mode should be suppressed.

Page 3: Bistable conditions

The f-d curve

• His thermal actuator has a 13mN of blocked force and 120 micron of free deflection at a temperature difference of 220 degC.

Page 4: Bistable conditions

Layout definition

Page 5: Bistable conditions

Mesh settings

Page 6: Bistable conditions
Page 7: Bistable conditions

• For simulation, one can not solve an arbitrary displacement directly, according to my experience. Instead, one need to increase the displacement bit by bit from zero, and telling Coventor to start the analysis from the result of the previous one.

• In this manner, the simulation will not fail easily, because defining the displacement resolves the large non-linearity of buckling.

Page 8: Bistable conditions
Page 9: Bistable conditions

100uN force (exaggerate 10 times)

Page 10: Bistable conditions

200uN

Page 11: Bistable conditions

300uN

Page 12: Bistable conditions

Wider beam: 10um wide

Page 13: Bistable conditions

Wider beam: 10um wide

• 1mN

Page 14: Bistable conditions

Wider beam: 10um wide

• 10mN

Page 15: Bistable conditions

100mN

Page 16: Bistable conditions
Page 17: Bistable conditions

Coventor simulation

• If I define the force and solve for displacement, I can never move on after I’ve reached the maximum force, even if I start from previous result.

Page 18: Bistable conditions

A beam with a initial apex height of 80 micron is simulated.

Page 19: Bistable conditions

• The simulation was done with a 5 micron step of the centre point displacement, ranging from 0 to 160 micron.

Page 20: Bistable conditions

10 micron

Page 21: Bistable conditions

80 micron

Page 22: Bistable conditions

120 micron

Page 23: Bistable conditions

160 micron

Page 24: Bistable conditions

Reaction force for 10 micron disp.

Page 25: Bistable conditions

Reaction force for 140 micron disp.

Page 26: Bistable conditions

Reaction force for 160 micron disp.

Page 27: Bistable conditions

Reaction force for 140 micron disp. (showing forces in opposite direction)

Page 28: Bistable conditions

That’s all. Thank you very much!