"Magnitude" of vibration response

[MikeyP]

I have an 3D linear model of a structure that is undergoing a steady state harmonic (single frequency) vibration response due to some harmonic forcing. It is a kind of FE model, but the modelling process is not really important.

The resulting time-varying displacement from its rest position of a point on this model is described by 3 phasors in the x, y and z direction.

x = X sin(wt + phix)
y = Y sin(wt + phiy)
z = Z sin(wt + phiz)

So the motion of the point over one cycle is an elipse in 3D space.

Question: Is there any kind of commonly accepted definition for the non-time varying "magnitude" of this vibration? If such a magnitude exists then how would you describe it's phase relative to the motion of some other point on the model?

The only sensible answer I can come up with is that it is possible to calculate the maximum deviation of the point from it's rest position (which you could consider as a "magnitude" of sorts). This does not resolve the phase issue (although this is of secondary importance).

Any other ideas?

Thanks

Mikey

--
Dr Michael F Platten

 

[electricpete]

If they are all the same frequency, then they can be added as vectors. The resulting displacement vector has magnitude sqrt(X^2+Y^2+Z^2)

Velocity - multiply by w
acceleraiton - multiply by w^2

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[electricpete]

I guess that's nothing new to you - the same as you said (maximum deviation from x=y=z=0)

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[electricpete]

It's a little more than that I guess.
These can be represented as vectors in space and time
x = X Re(exp j wt +Phix) Ux
y = Y Re(exp j wt +Phiy) Uy
z = Z Re(exp j wt +PhiZ) Uz
where Ux, Uy, Uz are unit vectors.

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[IRstuff]

I would think you'd need major and minor axes as well as tilt and orientation to fully describe an arbitrary ellipse in 3-D. You could potentially convert the former into a magnitude and eccentricity.


TTFN

FAQ731-376

 

[Denial]

If you are seeking the maximum deviation, it is certainly not as simple as merely Sqrt(X^2+Y^2).

Consider the two-dimensional case (Z=0). If x and y are fully in phase, then the max deviation is Sqrt(X^2+Y^2). But if they are 90 degrees out of phase, it is Max(X,Y).

Add the third dimension, and it becomes a lot more complicated.

 

[GregLocock]

Just to step back, I can't see how a linear model can produce that effect. Have you got sources and sinks in there?

The closest I've seen to that is where we have travelling waves superimposed on stationary waves, soemthing I've seen a lot of in acoustics, but not in vibration. Consequently no, I have no idea what terminology to use.


Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[MikeyP]

Greg,

If it were a normal mode I was looking at then, yes the motion from a rest position would trace out a straight line in 3D space by definition [Definition of a normal mode: all points move in phase or antiphase at the undamped natural frequency].

However, I am looking at what is effectively an operating deflection shape at a single frequency (a forced response to a single frequency excitation).

Our software used to have the "sqrt(x^2+y^2+z^2)" in it until we realised it was meaningless. So we took it out for the latest release - now customers are complaining that it is gone and I am looking for something to replace it! (we have included the option to view the magnitude in the direction normal to the surface instead)

I've worked out how to calculate the maximum deviation but I was just wondering if anyone knew of a reasonably widely accepted alternative.

M

--
Dr Michael F Platten