Designing a Cantilever Accelerometer with FEM

[nathanfan]

Dear everyone, this is my first post here. Nice to meet you all.

Now I have my project to design a catilever which can be used as accelerometer. The current stage is to have the vibration motion of the cantilever formulated using FEM, and then the design parameters can be substituted into the formula and check whether the natural frequency of the cantilever is within the expected region.

So my knowledge is only for the consistent mass FEM equation of the bar with uniform thickness and properties. I don't know how to formulate a cantilever which has a mass at its end, the mass would be dominating.

So what can I do? divide the cantilever into two elements, one without the mass while the other with the mass? If so, if I assume the cross-sectional area and density for both area to be identical ( in fact the mass would be a bit large and made by cast iron, while the beam would be made by aluminium alloy), would the error be so significant?

My stage now is a estimation of the dimension using the formula generated.

So thanks very much for the patience and kind participation.

 

[Darryl]

in not sure what a FEM is, but a simple accelorometer can be easy built, using a potentiometer, (pot). with a pendulum mounted on the shaft.
when you accellerate the pendulum swings towards you, (if its in front ofyou), and its resisticance will change, when you decellerate it will swing the other way, and (if zero'ed when motionless), will read negative.
then just buy a cheap logging multimeter, and either use a constant voltage source, or current source, or just read off the resistance.

this was a design i remember from a very old popular mechanics or popular science. (also you calibrate it using your car, with an assistant).

 

[AlephZero]

FEM = Finite Element Method, I assume. As in commercial computer programs like NASTRAN, ABAQUS, ANYSIS, etc, etc, etc...

Surely you are not going to model the cantilever by FEM by setting up the equations by hand, with just a 2-element model? You would get as good or better accuracy from a standard data sheet for calculating frequencies, e.g. see Roark "Formulas for Stress and Strain". If you really want to use FEM, get access to some FE software and create a realistic sized model, don't waste days of your time working out the numbers for a 2-element model by hand.

Having said that, the theory for modelling the tip mass with FE is easy. Just add the relevant translation and rotary inertia terms to the node at the tip of your beam :-)