How Do I Design a Solenoid?

Solenoid design is something of a black art. I'd advise you to look for something ready-made. Do you have any idea what force you need? What current can you go to (a major specification for solenoid selection is the power)?

I think your big problem is going to be the rate of operation - 100 Hz is very fast for a solenoid. Suspect it will have to be a high current job (not many turns of wire, to keep the inductance low, so high current to get enough force to do much good).

http://www.solenoids.co.uk/

GA

You didn't say what your process is. What do you have to move, or are you just vibrating something? Here's a cellphone vibrator that might work. Just Google.

Buy from any electrical store a miniature relay with coil voltage 12v DC. Discard the electrical contacts what remains is spring loaded magnetic plunger. Loud speaker and telephone devices are rated less than 12v and the coils will burn.

This reminds me of the time I decided to make my own Bass pickups for a custom Bass I fabricated. After building the housing and magnets, I set the frame on the lathe (after spending a couple hours to hold the frame) and began winding the 30ga magnet wire. After about 45 mins in I tried to go to a little higher speed, many several minutes later the wire broke. The pick up did work. In the end I went and bought some Dimarzio's for 1/2 the cost of what I spent on raw materials. The one I made didn't pass the on stage arena. Given the fact so many MFG's make solenoids, you would be much better off locating one that has an off the shelf design for your app. As I have gotten older (and hopefully wiser, or wizer) I have adopted the KISS method.

You must look for some kind of Vibrator, not really a solenoid, meaning that the moving part should be small and not like a plunger going into the solenoid. A small relay will give you the idea.

This being a vibrator, means that there will be a kind of spring return mechanism to resist the closure of the magnetic circuit and return the 'Blade' back for the next cycle.

Power: Depending on the strength of the spring, which will depend on the required PUNCH per cycle, your coil size/current etc will be determined...

http://en.wikipedia.org/wiki/Voice_coil

http://www.google.is/images?hl=is&q=voice+coil&um=1&ie=UTF-8&source=univ&sa=X&ei=n-JsTcCGJMOChQfNtJyPDA&ved=0CEoQsAQ&biw=1280&bih=899

automotive fuel injector

could strip down a door bell solenid and fir a small realy and timer to bring it on and off

I don't think you could get 100hz out of a doorbell solenoid.

If you are in the U.S., that low hum you often hear in a building is your 60hz electric power. 100hz is nearly an octave higher. Doorbells go ding-dong.

Hair clippers and a number of massage machines are 50/60Hz solenoids (of a sort)

"Doorbells go ding-dong" - not ones that go "Brrrrriiiiiiiiinnnnnnnngggggggg".

The continuous ringing sort generally work on the same principle as an electromagnetic DC buzzer.

When the button is pressed, a solenoid is energized which pulls in an armature against a spring. This action opens contacts in series with the solenoid, so the magnetic field collapses and the armature springs back (if it's a bell, it overshoots the rest position and strikes the bell). The circuit is re-made, and the armature pulls in again. (Note: sometimes the bell is struck on the pull stroke rather than the release stroke).

Would have to be a very light armature to get 100Hz, but it would work. An RC suppressor should be connected across the contacts to prevent arcing and electromagnetic noise emission.