Hi. This is a 1 DOF mechanical vibration question:
The normal approach is to use equivalence of Kinetic Energy to combine k1 and k2 into one spring. Then, the overall beam spring constant is found by combining the last spring with the previous combination. I have some issues with this method:
- Why are only k1 and k2 being combined using equivalence of Kinetic Energy and not k3 as well
- After the equivalence is calculated (here it is called keq1,2), why is this equivalence assumed to be in series with the last spring?
Please take a look at this for calculation of the overall beam constant: https://imgur.com/a/UiAAoxe
Now, once the beam constant is found, the normal formula for natural frequency can be used. However, since I had my confusions with the reasoning behind this method, I decided to use the simple approach.
My method:
I wrote the moment equations and solved using that method but the answer is obviously not the same. I cannot understand what I am doing wrong with my method. Here is my calculation:
As you can see, my answer is not the same as the one obtained by energy equivalence: https://imgur.com/a/zu0QbPF
I don't understand what I could be doing wrong here. Please let me know. Thanks!
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