I would like to build a small mechanism that will be able to move a smell membrane back and forth (around 5-15cm).
See video as example:
What will be simple but efficient way doing so?
Thanks
Magnet and coil as in the speaker obviously.
Can you elaborate?
There are a gazillion descriptions out there how speakers work, so @bluejets doesn't have to elaborate. I say it is you who need to elaborate what you wanna achieve here. Tell us things like frequency, medium the membrane will work in, how powerful should it be, the purpose etc.
Fair enough?
A small linear actuator would be the easiest way.
Fair Enough.
The membrane I use is like in the video I shared.
I try to achieve a mechanical mechanism that will replace the movement my hand is doing in the video which is to move the speaker back and forth on a straight line around 5 - 15 cm.
This seems perfect but the downside is the price that not so cheap. (I am planning to build 5 - 10 of those mechanism)
Ok, so membrane in y-axis and the whole speaker in x-axis, I got you. And it'll be on a flat horizontal surface like in the video?
Yes
What's the purpose, for us to get the bigger picture?
kind of a n sound installation. Imagine a small room filled with 5 - 10 object like this so it create interesting relations between the membrane sound
I'm thinking this effect could be done with a computer, how about that?
how so?
You could record one speaker while you move it like in the video, and loop it in several instances and output through the different speakers.
Have you ever seen one of these?
You made me listen to Deep purple now
Cool!! Thanks for sharing
I see what you say but it is not the same like the actual thing 
Yeah, the visual effect is part of the experience. How are the speakers to be arranged, in a kludge or spread out? On tables, the floor?