# Re: relationship between modal shape and forced harmonic response

hi, all,
> I have a question about the modal shape and the forced
> response of a structure.
>
> Let say once you have done modal analysis of a linear structure,
> for certain mode N, you will know the relative displacement between
> two points in this structure. Let denotes these two points as p1, and > p2.
>
> Then for the same structure, I excited it with a harmonic force and
> the excitation freq. is the Nth modal freq. The damping is defined
> by 0.1% modal damping. So, I will know the forced displacements > of p1 and p2.
It's most likely several modes were exicted not just one.
Is the forcing frequency approximately the same as the mode you
looked at.
I expect that the ratio of the forced displacements should be equal or
> very very close to the ratio I calculated based on the modal analysis > only.
> So, for the whole struture, the pattern of the forced response of this
> structure excited at Nth mode should be very similar to the pattern we
> see from the modal shape .
>
> Unfortunately, using a commerical FEM package ANSYS, I did not see
> what I expect. Is there anyting wrong with my understanding???
>
> Pls. help.
> Thanks a lot,
> William,
For any structure, if you are investigating mode "N" at frequency "F", if you modeled the structure perfectly, the analytical and physical would match perfectly. This is relatively easy to do with simple structures-in fact, with a simple beam, or even a truss, you should have no problems. AS the structure gets more complex, the more likely an error will creep in-sometimes BIG errors! A couple of things to look at: 1. do a random sweep with your force device. Check for resonant frequencies. Are any close to what you calculated? 2 Do a Kinetic energy check with the analytic model. Do you have your acclerometers in places which will actually define the mode? Make sure you are forcing at a point which will help define the mode. If you are forcing on a near-zero elative deflection point, you just won't get there... I would almost bet that the sweep will reveal mode frequencies in reality that you don't have analytically. You really need to do a full-blown modal survey, in all likelyhood.
Jeff F> snipped-for-privacy@hotmail.com (William Lu) wrote:
yes, the forcing frequency is exactly the same as the mode i looked at. but the mode freq is calculated without considering damping.
Roger, Thanks a lot for reply. Actually, I have not done any experiment. All I have done is numerical calculation in computer only.
For modal analysis, I did not consider the damping matrix, for mode "N", let say, I see the point 1 and point 2 move out-of-phase, since the "amplitude" of these two points in the Nth modal shape for freq. "F" have the same value, but opposite signs.
Then, I apply unit force at somewhere on the same structure, and do harmonic repsonse calculation. I considered the damping matrix, of course. The excitation freq. is exactly the same freq. as the Nth mode freq. I see the point 1 and point2 have exactly the same vibration amplitude and also phase. So, point1 and point 2 now are vibrating in-phase, instead of what we saw from modal analysis, out-of-phase.
I understand that for Nth mode, there could be adjacent modes affecting the vibration behaviors. But it is still strange why a out-of-phase vibration seen in modal shape was exactly changed to in-phase as seen in harmonic response calculation. Please advise.thanks
I would have to see the analysis to be certain, but consider the following situation in a long, reasonably slender beam, simply supported at the ends. Mode 1 us going to replicate the static deflection-it will be a simple arc up and down at the extremes of motion. mode 2 will look like a full sine wave, mode 3 a sin-and-a-half, etc. If you impose a force on the structure somewhere, of a duration to excite mode 2, for example, you will also excite mode 1 to a certain extent. Depending on the flexibility (1/k) of the structure, mode 2 superimposed on mode 1 can have your 2 points displaced on the same side of zero (steady state), and yet still be out-of-phase. I'll try to depict that below: ____ / p2 / \ p1 \ / \ Mode 1: / \
mode2/1 ______/\__/\________Steady State mode 2 / \/ p2 p1 \ / \ / \ Ok-it's a lousy sketch, but I hope it gets the idea across-- This is not an infrequent occurrence. The programs all do this-and it does reflect reality pretty well.
Roger
William Lu wrote:

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