# Mode shapes of a beam

I have never been able to grasp why certain mode shapes are the way they are. For example, I ran a free vibration analysis on a vertical beam fixed at the ground. The second mode shape is vertically straight. This is the same case whether or not I have a lumped mass at the top of the beam. Any thoughts on what would cause a mode shape to be vertical?

## Answers and Replies

AlephZero
Homework Helper
For example, I ran a free vibration analysis on a vertical beam fixed at the ground.

The clue might be in the two words "free" and "fixed". Your beam could be either one or the other, but it can't be both at the same time.

OldEngr63
Gold Member
So, are you talking about the vibrations of a flag pole column, with and/without a tip mass? Is that the situation you are trying to analyze here?

I'm analyzing a water tower. I have three cases that I'm looking into no lumped mass, 20,000 lb, 40,000lb. For each case I use a solid and hollow cross section for the tower. So all together I have 6 runs. For all the runs that have a lumped mass, the second mode is vertically straight. Without a lumped mass I get a curved mode shape. I'm trying to figure out why this is.

OldEngr63
Gold Member
It is pretty difficult to understand what you mean by "vertically straight." What is the deformation shape then? What direction is the vibrational displacement?

The vibrational displacement is to the left and right. What I mean by vertically straight is that it is perfectly vertical.

OldEngr63
Gold Member
If the static equilibrium position is straight up, then the lateral vibration modes will appear as displacements about this vertical position. The mode shape is always superimposed upon the static equilibrium position.