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(ABAQUS CAE) piezoelectric analysis

Hello. 

I'm doing piezoelectric analysis using abaqus CAE v6.12.

Specifically, what I'm doing now is to make the bimorph piezoelectric harvester model using Abaqus CAE

and to validate my model.

My FE model is made based on the model developed by A Erturk and D J Inman in their paper,

'An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations'

They presented the analytical solution for voltage output and experimental validation is also presented in this paper.

As I mentioned before, my current goal is to validate my FE model by comparing the simulation results with the results from the above paper.

Actually, I've succeeded to get the correct results with respect to the first natural frequency and the overall trend of voltage output of my simulation is also pretty much the same to above paper. 

 

But, my problem is from here.

In Erturk and Inman's work, the experimental measurements are repeated for 8 different values of load resistance, i.e. 1, 6.7, 11.8, 22, 33, 47, 100 and 470kΩ as can be seen in attached figure. Each of the resistive loads results in a different voltage ouput as well as different first natural frequency.

My question is how to define this different values of load resistance (R in the figure) for piezoelectic analysis in abaqus.  How can I describe the different values of R?

 

I tried with a bunch of different ways.

One of them was to change the material property, i.e., 'Electrical conductivity' in 'Property' module. But, it didn't affect the result at all. All the other ways didn't give me the good results as well.

Please share your experiences. Any advice would be tremendous help for me.

 

Thank you for reading my post. Thank you so much.

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