# Homework Help: Piezoelectric and minimum dimensions of an actuator beam?

1. Nov 25, 2014

### mikehsiao789

1. The problem statement, all variables and given/known data
We want to build a micro-positioning system that produces a maximum travel of
5 μm by using a piezoelectric linear actuator beam with a square cross section (a^2) and length (l) as shown below. A piezoelectric material with piezoelectric
coefficients d13 = -2.0×10-8, d33 = 5.3×10-8, d24 = 3.7 ×10-8 and d25 = 4.1 ×10-8
cm/V ( Si = djiEj ) and a dielectric strength of 106 V/cm is used.

For a maximum power supply voltage of 110 V and a safety parameter of 1.5,
find the minimum dimensions of the beam (a and l). Explain which direction
for electric field is the most effective for creating the required linear travel and
how we should place electrodes to apply such field to the actuator beam.

2. Relevant equations

S= Dij Ei,

3. The attempt at a solution
I wrote the piezoelectric matrix (s1... s6) = YT + ( d12.... d15,... d51... d55), however I am not sure what to do with the dielectric strength and what equations I would go about doing this...

2. Nov 30, 2014