Piezoelectric example problem

NAP2626

Hey I am looking for an example problems that have piezoelectrics generating electricity.

I would like to have and use a simple problem in which a piezoelectric is squeezed to generate electricity. Does anyone know where I can find such problems and solutions?

NAP2626

I was thinking something a long the lines of;

You have a 1000 N force striking a block of PZT that has a 20 cm by 20 cm area and that has a thickness of 3 cm. How much voltage and power is created.

What you know: Youngs mod, piezoelectric coef, relative permitvity, etc.

Step 1) Calculate change in thickness using
Delta t = (Force * thickness)/(youngs mod *area)

Step 2) with delta t you can figure out strain using
Strain = delta t/t

step 3) With Strain figure out stress, recall we know youngs mod;
Stress = younds mod/ strain

Step 4) D= d*T; piezoelectric coefficent * stress = Columbs/m^2

Step 5) Get charge q: columbs/ m^2 * area (m^2) = charge columbs

Step 6) Capactience; (Relative permit * permit of space)*( Area/ thickness)

now finally Step 7) Voltage: V= Q/C so you take the charge calculate in step 5 and divide it by the materials capacitence calculate in step 6.

Let me know what you guys think or if this is the correct approach. Also how would I calculate the internal resistance of the material so that I can take the voltage use that resistance to caculate current and power.

Any insight or corrections would be great