"Magnitude" of vibration response
"Magnitude" of vibration response
(OP)
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
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





RE: "Magnitude" of vibration response
Velocity - multiply by w
acceleraiton - multiply by w^2
=====================================
Eng-tips forums: The best place on the web for engineering discussions.
RE: "Magnitude" of vibration response
=====================================
Eng-tips forums: The best place on the web for engineering discussions.
RE: "Magnitude" of vibration response
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.
=====================================
Eng-tips forums: The best place on the web for engineering discussions.
RE: "Magnitude" of vibration response
TTFN
FAQ731-376: Eng-Tips.com Forum Policies
RE: "Magnitude" of vibration response
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.
RE: "Magnitude" of vibration response
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
SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: "Magnitude" of vibration response
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