Hi, explain a bit more what exactly u r looking for. The electric field generated thru piezoelectric effect is assumed uniform over the thickness of piezo.E=1/tp; where tp=thickness of piezo. The capacitance of piezo will also depends on its dimensions (area). What kind of structure you are working on? You can download my article "material..." and see the equations where the dependence of terms in governing equations on dimensions is given. U can understand from those formulae. All the best. 

The area cannot be directly related to the voltage but the rate of deformation in the stretcher which is related to the dimension of piezo can be related to the generated voltage. So the geometry of the crystal and rate of deformation is very important.  

The generated charge density under conditions approaching a short circuit is given by

     (n = 1, 2, or 3)                       

The mechanical axis, n, of the applied stress or strain by convention is

1 = length or stretch direction

2 = width or transverse direction

3 = thickness direction

Where D = charge density developed, Q = charge developed, A = conductive electrode area, = appropriate piezoelectric coefficient for the axis of applied stress or strain, n = axis of applied stress or strain, = stress applied in the relevant direction

The open-circuit output voltage  is given by

    (n = 1, 2, or 3, as above)              

Where g = appropriate piezoelectric coefficient for the axis of applied stress or strain, = applied stress in the relevant direction, t = the film thickness

Hope this will help

The voltage is independent on the surface of the electrodes. For a given deformation you will have a certain electric field in open circuit conditions. Then for a parallel-plate capacitor configuration you multiply by the thickness and you get the voltage. In the short circuit case, for a given deformation you have a certain dielectric displacement, which, for parallel-plate structures, is equal to the surface charge density. To get the total charge then you need to multiply by the surface.

Hi Karthik,

From the details you have mentioned it seems that you are using the piezo actuator to induce vibrations in the structure. Am I right? If so what is the purpose, is it for structural health monitoring? Your discussion title give another impression that you are using the piezo element for energy/signal generation. 

In general the voltage required/generated is directly related to the thickness of the actuator element between the electrodes. The force generated by the actuator depends on the area and in opposite case the area as well as the rate of application of stress and area determines the polarization and hence the current/signal the piezo element can generate.

You can refer to any standard books on piezo electric sensors and actuators to gain more insight it the characteristics. There are several journal articles that referrers to  both structural as well as energy harvesting application for piezo elements.

Regards,

Dileep

yes A(Area) has effect on capacitance of piezoelectric materials   

Dear Karthik:

Yes, there is a relation between the forces & velocities in the surface of a piezoelectric device and the applied  / generated voltages at its electrodes. And this relation depends on the surface area. In the attached file, I am sending you a resume of this rather complex relation, which can be particularized for each one of two processes: -direct and inverse- piezoelectric behaviors.

A complete explanation of these relations could be found in the Chapter 4 of the book ... "Piezoelectric Transducer and Applications". Titule of this chapter: " Models for piezoelectric transducers used in broadband ultrasonic applications", by: JL San Emeterio, A. Ramos and A. Ruiz, pp.187-203. Edited by Edit. SPRINGER-VERLAG. 2008. Berlin. 

If you send me your e-mail address, I could give you a copy of this chapter.

Regards,

A. Ramos

Thank you Sir....My e mail address is [email protected]

Dear Karthik:

I have sent you an e-mail with a copy of  that chapter, I had recommended to you,

in relation to your question related to: "any possible relation between the forces & velocities in the surface of a piezoelectric device and applied / generated voltages".

I hope that this chapter could be of your interest, in order to solve the problem.

Regards,

Antonio

Dear Karthik:

I have sent you an e-mail with a copy of  that chapter, I had recommended to you,

in relation to your question related to: "any possible relation between the forces & velocities in the surface of a piezoelectric device and applied / generated voltages".

I hope that this chapter could be of your interest, in order to solve the problem.

Regards,

Antonio

Hi following is the simple model of piezoelectric material. It's not considering any extreme conditions.

Vz = Q/C; Q is charge and C is capacitance. This is standard formula for capacitance.

Qz = dzz* Fz or Qz = dzx * Fx (doesn't matter as long as you get charge in z direction.

C = (er * eo * A) / t ; er is relative permittivity, e0 is permittivity of free space. A is cross-section Area and t is thickness

With some substitutions you get:

Vz = (t * dzz * Fz) / (er * e0 * A)

This leads to basic intuition that smaller Area and larger thickness leads to larger instantaneous voltage.

Dear Jayanarasimhan

I recently derived a formula that relates the applied pressure to the output voltage. It is V=P/ne, where is electric charge, n is the number density and P is the pressure.

Arbab