Discussion Forum

Hi,

In eigenfrequency, the displacement value doesn't have any meaning. To get a correct it, you need to use Frequency domain instead of eigenfrequency study.

You setup the range of frequency including the resonant frequency.

Thanks Kim.

I obtained a set of 6 eigen frequencies. When I study the details in frequency domain (did a sweep in the eigen frequency range) the graph displacement vs frequency shows me just the 1st and 5th harmonics. I wonder why the rest of the harmonics (2nd, 3rd, 6th...) do not show up. Even i tried zooming as well as fine sweeping to see any small peaks of resonance but there is just a slope of line, no resonances found.

Is there something I am missing or any other way is needed to find out the displacement at each eigen frequency?

Please help.

Best,
Shubham

Hi Shubham,

Probably your load in the frequency sweep does not excite the other modes. Say you are working with a beam in 3D. Then there will be eigenmodes for bending in two directions, axial motion, and torsion. If you the run a frequency sweep with a single transverse load, then it can only excite one of these four types of modes.

Similarly, if you have a symmetric structure, a symmetric load can only excite the symmetric modes, not the antisymmetric modes.

Regards,
Henrik

Hi Henrik,

Thanks for the response. I am dealing with a 3D square shaped structure in which am applying a constant static load from top (-z direction) of the structure and a harmonic perturbation/point load at the center from bottom (+z direction). Is it because of this symmetry that I am not able to excite other resonance modes? Is point load at the center works or I will have to apply harmonic load to the boundary surface from bottom?
However if I apply harmonic load to one of the corners it does show a peak for 2nd mode. But I think the displacement value is not accurate in that case.

What is the other way to calculate displacements for each eigen modes? Please help.


Best,
Shubham

There seems to be a fundamental understanding of what an eigenmode analysis gives. Since this seems to come up from time to time I will try to help.

An eigenmode is a solution to the governing equation, satisfying all boundary conditions, in which all parts of the system have displacements at the same frequency. The amplitude and phase of the displacement will of course vary from location to location.

If a system is excited in one of its eigenmodes it will continue to vibrate in that eigenmode forever, with no displacement at any frequency corresponding to any other eigenmodes.

Exciting a particular eigenmode (only) can be accomplished if all points are given the right displacement or velocity. The eigenmode solution tells us what those displacements are.

THE ABSOLUTE VALUE of the eigenmode solution is meaningless. Only the relative values between different points is meaningful.

As an example, consider a vibrating string between two supports. A half sine wave is an eigenmode. It is an eigenmode independent of its amplitude. An entire sine wave is also an eigenmode, Again, the amplitude is irrelevant. (Of course, neglecting nonlinearity.)

So we come to the problem of exciting particular eignmodes. Suppose we pull the string at a point exactly halfway between the two supports and then let it go. (So before letting it go the string is triangular in shape). If we call the lowest mode f0, then the string will vibrate at particular frequencies, f0, 3f0, 5f0... It will not vibrate at 2f0, because this eigenmode is antisymmetric about the centerpoint and the excitation is symmetric. (There is a Fourier transform involved here).

So whether a particular eigenmode is excited depends on WHERE the disturbance is, and the symmetry of the disturbance.

The eigenmode solutions DO provide insight into the types of disturbances that will excite a particular eigenmode. If a particular mode does not appear in a frequency sweep of the disturbance, it is because the symmetry or the location of the disturbance is such that that particular mode is not excited.

Hope this helps.

D.W. Greve
DWGreve Consulting

Thanks Greve for such insightful details.

I am designing a square shaped diaphragm 100*100*3 mm^3 (precisely, a prestressed mirror shape as in one of COMSOL example) which has a constant atmospheric load of 100kPa from top (+z-axis) and a harmonic perturbation at the center of 25mN from bottom (-z axis). Its boundaries are constrained. I am using isotropic loss for now with Q=10 (just assumption).

I have done a prestressed eigen frequency study and obtained the resonant frequencies. My aim is to make sure that the diaphragm motion (bulk) is in z direction and other modes (in axial and torsional) do not vibrate much and so these modes can be eliminated later as far as one can diminish their impact with more innovative designs.
I have been trying to calculate the amplitudes of the eigen modes but as pointed out by you that their absolute values are just meaningless. Is there any way around to achieve my result expectations/conditions. May be am going the wrong way, not sure though !

Best,
Shubham