Hi everybody

I read this paper:

**Finite element analysis of Cymbal piezoelectric transducers for harvesting energy from asphalt pavement**

In this paper, The governing equations of piezoelectric is:

Where t_{p}=2mm,Diameter(D)=32mm and piezoelectric material is PZT 5H.

As far as I know ε_{0}= 8.854 pF/m.

in paper relative dielectric constant at constant strain is:

From simulation in abaqus i get the V=96.98

they mentioned In paper:

The electric potential is about 97.33V of the design Cymbal. 0.06 J electric energy can be storage in that Cymbal.

Then U is: 0.06 J

Now my main question is how can i calculate the ε^{T}_{r }?

Because U is the final answer. and when i put all variable in eq 8. and pick Dielectric Constants, @ 1KHz, 3500 from this site (for material: PZT-5H):

https://www.steminc.com/PZT/en/piezo-materials-properties

My U will get this:

**U=5.9024e-05**

As you can see There is a lot of difference.

By the way if i put relative dielectric constant at constant strain matrice in eq 8. how can this possible , one side is scalar and other side is matrices ?

With best regards.

yassou.

## Comments rated to be Good Answers:

Re: Calculation of Relative Dielectric Constant of Piezoelectric?" by Rixter on 11/10/2017 10:48 AM (score 2)