# Help with modelling a piezo

I'm using the Van Dyke model from this article and I'm a bit lost on a few things.

1. Since the only nodes I can physically connect to are the ends, can I assume that I am limited to the voltage across the parallel capacitor?
2. I have derived the following equation for this network: $$\frac{d^2i}{dt} + \frac{R}{L}\frac{di}{dt}+\frac{1}{LC_1}i_1 = \frac{1}{LC_o}i_o$$ Going back to #1, I guess I'd only need to solve for the right half of this to get the transient response. But this is simply a tank circuit now, which negates the rest of the piezo circuit.

what is the proper way to model this in a circuit? I want to model a piezo to see it's response to a pulse.

thanks.

EDIT:

A little more context on the problem I'm having. here is what I want to model:

The switch closes momentarily and opens. A measurement on an oscilloscope shows this:

The main resonance is the larger one - the other ones are assumed to be reflections within the medium. Ultimately, I would like to create a model for this behavior.

• I'm not sure about your equation. Won't R_1 and L_1 only see current i_1? And some other equation i=i_0+i_1. – George Herold Jun 14 '17 at 12:25
• What do you mean by response to a pulse? Please define input (pulse source) and output. Possibilities are electrical voltage and current, mechanical displacement, mechanical velocity, mechanical force, acoustic pressure,... – JLo Jun 14 '17 at 13:24
• Get a piezo data sheet and look at the model. I've seen a few data sheets that have models. – Andy aka Jun 14 '17 at 17:44