# Beam boundary conditions

1. Nov 13, 2015

### Ben9622111222

Hello,

Can anyone help me find the boundary conditions of the below given beam please. Its a clamped-free beam but the overhanging sectiona and the mass makes it confusing. Actually I am puzzled about finding the initial conditions.

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2. Nov 13, 2015

### SteamKing

Staff Emeritus
It's not clear what type of analysis you want to perform on this arrangement.

Based on what little information you have provided, it appears you have two overhanging beams, one of which has a mass attached to the end. If you want to do a static structural analysis, you can treat each beam independently. If there is some vibration analysis going on, the method of clamping may need to be considered.

3. Nov 13, 2015

### Ben9622111222

Yes. I am doing vibration analysis. Do you suggest pinned arrangement instead?

4. Nov 13, 2015

### SteamKing

Staff Emeritus
I'm not suggesting anything at this point. I'm just trying to understand what it is you're looking for.

5. Nov 13, 2015

### Ben9622111222

You can see, that the initial conditions here are easy enough to get and also proceed forward. In my case its not, due to the overhanging section

I am trying to make an equation like equation 10 in the above link for my system.

6. Nov 13, 2015

### SteamKing

Staff Emeritus
Is there any forced excitation of this beam? If so, where is it located?

7. Nov 13, 2015

### Ben9622111222

No there is no forced vibration. The rod is flexible, and it is rotated by a motor. the motor position is the clamped support shown. So when the rotation stops there will vibration at the tip. to modal this, I need to find the beam boundary conditions.

8. Nov 13, 2015

### SteamKing

Staff Emeritus
You need to 'model' the beam.

Well, you have certainly been keeping things close to the vest here. Based on your earlier posts, I never would have guessed you were looking at a rotating shaft.

Since the motor is located at an intermediate point in the shaft, each portion of the shaft will have two different static deflection curves, based on the loading conditions of the beam. When the beam starts to rotate, a whirling vibration will be set up. The critical speed of the shaft can be estimated by applying the Rayleigh method or Dunkerly's method.