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calculating the spring constant of a rectangular cantilever
Posted Sep 22, 2011, 7:23 AM EDT Modeling Tools, Parameters, Variables, & Functions, Structural Mechanics & Thermal Stresses 2 Replies
i'm currently simulating a cantilver used in atomic force microscopes. I'm then calculating the spring constant of a cantilever using Hooke's law and the z-displacement caused by a load.
There is a another well established method to calculate the spring constant k of rectangular cantilevers based on the Young's modulus and the geometry (see e.g. Chen, Yeh, Tai, Anal. Chem. 79, 1333, 2007):
k = ( E * w * t^3) / (4 * L^3)
E: Young's modulus E=78.7GPa
t: thickness t=0.41mm
w: width w=0.24mm
L: length L=2.94mm
Pluging the values mentioned above in the formula you get k=12807 N/m.
Modelling a cantilever of the same properties using Hooke's law and the z-displacement i get k=12669 N/m.
So both methods yield consistent numerical values.
Unfortunately when i double the width i get:
k=25614 N/m using the geometrical method
k=22190 N/m using Comsol
This is a way bigger mismatch than before, which i'm unable to explain physically.
Therefore i'm asking for your help. Since i'm started using Comsol only a few weeks ago, i might used odd parameters or forgot to take something important into account. Basically i think my inexperience with Comsol is causing this mismatch.
I'd appreciate it if you'd take a look into it.
Because the file sizes are too big to attach i uploaded them here:
The .rar contains both cantilever (width 0.24mm and 0.48mm)
I'm sorry for making you download them, but if you need another hoster or if you'd like me to send them to you via email, please let me know.