Total elongation of differently shaped "springs"

[Jesus Ibarra]

Hello!

First of all, my field is not Mechanical Engineering but Nanotechnology so I apologize if I use very basic terms.

I am currently working on the design of an in-plane optical MEMS accelerometer. The idea is: a waveguide is built within the structure so that when the MEMS is accelerated due to external forces, there is elongation of the waveguide which leads to a phase change in the light signal with respect to a reference one. With this phase change one can measure the external pressure.

We will ignore the vertical direction and consider only an xy plane. The system consists of one mass held by four springs restricting movement only in one direction. I mean, there are two springs on one side and two on the opposite leaving two ends free. It is a symmetrical system and the springs act in parallel so one can model the system as one spring acting on the mass. With this approximation one can find the spring constant and displacement in the free direction. I am trying to model springs with different shapes (like "crab-legs" or "serpentine"). Spring constants even for these more complex systems can be found. My problem however, is that I also need the total elongation of the system of beams (that are being modeled as springs) which is the driving factor for phase change of the light that goes through the waveguide. I am kind of lost and I am not even sure how to search in literature (I have spent quite a lot of time doing research). Should consider each beam forming the spring completely separate and calculate elongations in both x and y directions for each one of them? How could I approach this problem? Any suggestions or comments are welcome.

The image that the link shows, is more or less a representation of the physical structure. However, in my design, there are two springs instead of one on the "fixed" sides.

Thank you all.

The image is not loading in my "preview" option. So here is the link in case it doesn't appear:

https://www.google.be/search?client...0k1j0i24k1.0.bqjiKO0cP_A#imgrc=QmAKKv4oYVrWOM:

 

[jrmichler]

With a system like yours, it is usually best to analyze the entire system as a system. With complex springs such as shown in the link, it can be difficult to find an accurate equation. You might be better off to model it and use FEA. A package like SolidWorks can model up a spring, then take that directly into integrated FEA. With a proper model, you can test 5 to 10 iterations per hour. One day, and you will have a complete design table. The learning curve will be about a week.