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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: enter image description here

The switch closes momentarily and opens. A measurement on an oscilloscope shows this:enter image description here

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.

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  • \$\begingroup\$ 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. \$\endgroup\$ – George Herold Jun 14 '17 at 12:25
  • \$\begingroup\$ 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,... \$\endgroup\$ – JLo Jun 14 '17 at 13:24
  • \$\begingroup\$ Get a piezo data sheet and look at the model. I've seen a few data sheets that have models. \$\endgroup\$ – Andy aka Jun 14 '17 at 17:44

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