Piezoelectricity Calculations

Sure thing. I took a class on this my senior year (2006). You are right that the calculations can get complicated, but the basics aren't too bad.

I checked out the wikipedia entry, and the background info and math are correct (http://en.wikipedia.org/wiki/Piezoelectricity).

Basically, the piezoelectric effect is a coupling between the mechanical and electrical domains, or properties, of the material. The equations used predictably turn out to be a set of coupled equations, one describing the electrical domain and another the mechanical. They are called 'constitutive equations'. Both equations include T, stress, and E, electromagnetic field strength terms (therein lies the coupling...). The equations are matrix equations that can get big and complicated due to varying material properties in each direction, etc., but they are simple for what you want to do. As the wikipedia entry describes, when you only look at one direction, many terms go to zero and make your life easier.

The wikipedia entry has some good external references that have material properties for various materials and more in depth descriptions of the math. I'm sure you could find some calculators online that will do most of the work for you. If not, break out an old text book and review matrix math - there are some simple tricks to solve sets of simultaneous equations like these.

If you can't find good enough details online, there are decent text books around (look for latest release date) and any company that supplies the materials should be willing to walk you through it in more detail. You can also try a google scholar search for publications that might help.

From a purely practical standpoint, you can get an idea of what you want if you just look at off the shelf actuators and sensors. Their data sheets will have a simple description of what you are asking for.

All the math basically holds for materials with other domains coupled, or more then 2 coupled, like magnetic field or optical characteristics. There are some crazy materials out there.

Dear Butcher

Thanks for the pointers and the advise. I need to get to a prototype ASAP and all your comments are great for achieving that. I do envisage however a lot of tweeking from that stage on. I did look at off shelf products but signal speed seemed to be a problem. The invention I'm working on at the moment has a 'real time' response to an almost ultra sonic event and I need to get as close to that in signal speeds. So function/operational speed is in there as well.

I wish my brain could do the same thing.

Thanks again,

KennyT