# Vibration problem: mode shape?

1. Jan 21, 2008

### hanson

Hi all. I am taking a course in mechanical vibrations.
I know that a mode shape is a pattern specific to a natural frequency of a system.
That maens, the mode shape is determined under the context of free vibration, right?
What kind of information can we obtained from the mode shape?
Is the "mode shape" basically telling us how structure will vibrate, in what pattern, right?

But I am also confused that, will the "mode shape" play any role in forced vibration?

Let's say the structure vibrate in mode shape 1 at natural freqyency 100Hz.
Will the structure vibration with a "similar shape" when it is under forced vibration of frequency, say, 125Hz or 80Hz? I don't know the answer because in my mind, mode shape analysis is only valid for free vibration.

Lastly, in the way can we excite the structure to get different mode shape? Is it firstly by forced vibration at a frequency close to the natural frequency?

2. Jan 21, 2008

### FredGarvin

Forced or free vibration, it doesn't really matter if the boundary conditions remain the same. For example, the common lab project to study this is a flexible cantilever beam. You the excite the clamped end of the beam. By walking up in frequency of the excitation source, you can dial in the natural frequencies and see the mode shapes happen.

3. Jan 21, 2008

### Staff: Mentor

You have it right, hanson. What you are missing about forced vibrations is simply that since there are different ways an object can vibrate, applying the exciting force in different ways (in different locations or at different frequencies) can excite one or more of the mode shapes.