# Natural Frequency and mode shapes

by skaboy607
Tags: frequency, mode, natural, shapes
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 P: 107 Hi I am using Ansys to find the natural frequency of a structure but this has meant that my understanding of vibrations has become unstuck. When I last studied natural frequencies, it was under free vibration. I formed the impression that one structure can have only one natural frequency which would correspond with a mode shape. However, in Ansys, for a continous structure, you can find an infinite number of mode shapes (default of 6). So my question is, how can a structure have so many natural frequencies and therefore corresponding mode shapes. Confused me! Any help much appreciated!
 Sci Advisor Thanks PF Gold P: 12,261 I could ask why there should be only one mode shape. The simple model of two nearly identical masses on nearly identical springs, coupled by a third, weak spring, has two modes. A taught string can have a vast number of overtones. So why shouldn't a complex structure have loads of possible modes of vibration?
 P: 107 You could yea but that would only make me ask more questions and not answer my OP?
 Sci Advisor Thanks PF Gold P: 12,261 Natural Frequency and mode shapes I have at least given you a reason to think that there can be many modes. It's acceptable to answer a question with a question because, in my question, there is a route to the answer to yours. You didn't want spoon-feeding did you? Do you not watch any of those Mystical Eastern Combat films? They never get straight answers there either but they end up being able to fly.
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 Quote by skaboy607 When I last studied natural frequencies, it was under free vibration. I formed the impression that one structure can have only one natural frequency which would correspond with a mode shape.
Wherever you got that idea from, it's wrong, unless you were considering models with only one degree of freedom (a mass on a spring, a simple pendulum, etc).

 However, in Ansys, for a continous structure, you can find an infinite number of mode shapes (default of 6).
There is nothing special about Ansys here (except the arbitrary choice of getting 6 modes by default).

If a structural model has N degrees of freedom, it will have N natural frequencies and mode shapes. For a finite element model, N is usually equal to the number of unconstrained mesh points in the model, times the number of degrees of freedom at each mesh point, which might be 3 or 6 depending whether or not the finite elements have rotation variables.

Actually that's a bit over-simplified, but the bottom line is that most real-life FE models will have a very large number of natural frequencies and mode shapes, Only the lowest frequencies will be accurate enough to be useful, so it would be pointless (and it would take an unfeasilbly long time) to try to find all of them.

Mathematically, the equations of motion of a continuous flexible structure have an infinite number of vibration modes.
P: 107
 Quote by sophiecentaur I have at least given you a reason to think that there can be many modes. It's acceptable to answer a question with a question because, in my question, there is a route to the answer to yours. You didn't want spoon-feeding did you?
Yea that was what I was kinda hoping but as we've gone done this route, i'll roll with it. I have hard time getting to grips with this. Is a mode shape at a single instantaneous point in time, i.e. to use your string example, it is plucked, for each moment in time , there is a mode shape until it comes to rest?

 Quote by sophiecentaur Do you not watch any of those Mystical Eastern Combat films? They never get straight answers there either but they end up being able to fly.
No I can't say that I ever caught those!

 Wherever you got that idea from, it's wrong, unless you were considering models with only one degree of freedom (a mass on a spring, a simple pendulum, etc).
Yes it had only one DOF and it was a mass spring system excited from a plate underneath.
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 Quote by skaboy607 Yea that was what I was kinda hoping but as we've gone done this route, i'll roll with it. I have hard time getting to grips with this. Is a mode shape at a single instantaneous point in time, i.e. to use your string example, it is plucked, for each moment in time , there is a mode shape until it comes to rest? No I can't say that I ever caught those! Yes it had only one DOF and it was a mass spring system excited from a plate underneath.
What do yo mean by "a mode shape"? The shape of the system, at one instant, will be the sum of all of the oscillations from all the modes as they appear at that time. A plucked string will give a sound which is a combination of many of its natural modes so they are all present. (The relative amplitudes will depend on how and where the string was plucked). The shape will keep changing.

Even 'Karate Kid' has some of that nonsense in it, I think. I wouldn't suggest you take time to see it if you haven't but Crouching Tiger is worth seeing. Never a straight answer in the whole film.

Of course, if your system has only one DOF, you couldn't expect more natural frequencies but you asked in general so you got the general answer ( / question).

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