Harmonics are whole number (1,2,3,....N) multiples of any fundamental forcing frequency. In rotating machines these fundamental forcing frequencies are most often generated and directly related to the RPM of the machine and/or the electro/magnetic forces within the motor.
Modes are the natural frequencies of a component or a system of components.
"Modes are a characteristic pattern in a vibrating system, All peaks reach their maximum displacements at the same instant. "
No, not in real systems. You get complex modes where the phase angles are not exactly either 0 and 180 degrees.
I would be interetsted to read if if people think that these occur due to poor fitting technique, or are fundamental properties of real systems. I suspect the latter.
We must be careful here with the technical terms. The quote you posted:
"Modes are a characteristic pattern in a vibrating system, All peaks reach their maximum displacements at the same instant. "
Should read "NORMAL modes are a characteristic...".
Normal (as opposed to "operational", "damped" or any other kind) mode shapes are what we are (usually) trying to find in experimental modal analysis, often so that they can be comapared directly with normal mode shapes obtained from an FE model for validation purposes.
The complexity often seen in mode shapes identified from measured data can come from various sources.
1) Non-linearity. Normal modes have no meaning in a non-linear system so it is unsurprising that standard linear analysis methods fail.
2) Rubbbish or noisy data. Enough said.
3) Inadequate test methods. A measurement taken using a single exciter may not be able to distinguish modes which are close together in frequency. A special case of (2) really.
4) Inadequate analysis methods. "Single DOF" analysis methods (for example Nyquist circle fitting) cannot separate modes which are close in frequency (the Nyquist plot is not a circle!). The problems associated with (3) and (4) can be minimised by using multi-input-multi-output testing techniques and Global multi-DOF analysis methods (eg Polyreference).
5) The most likely explanation. If all of the above do not apply then the reason for the complexity is almost certainly NON-PROPORTIONAL DAMPING. I have posted stuff about this before. Briefly, proportional damping is where the damping (C) of all degrees of freedom is a linear combination of the mass (M) and stiffness (K).
i.e. C = aM + bK, where the constants of proportionality (a and b) are the same for ALL degrees of freedom.
This is often known as Rayleigh damping. There are more precise definitions but their physical significance is not clear so I won't quote them here.
When the damping is proportional, every mode is uncoupled from every other mode. The system response is a superposition of the responses of the individual modes. No energy is transferred between modes.
Generally of course, real structures do not have proportional damping. In NP damped systems, energy IS transferred between modes. The principle of a modal damping value for each mode is no longer valid. Now when we apply our curve fitting analysis to our measured data, we have a problem. The first part of a Polyreference type analysis is to find the natural frequencies and modal damping values for each mode. The curve fitter does its best with the available (NP damped) data and duly spits out these values. In the second stage of the analysis, the curve fitter takes thes natural frequencies and dampings and attempts to find suitable mode shapes so that the identified modal model fits the measured FRF data. However, because a simple modal damping value is not enough to adequately describe the damping behaviour of the system, the curve fitter is forced to "fudge" the mode shape in order to make the measured and predicted FRFs match each other. This fudge manifests itself and a complexity in the identified modeshape.
There is a family of analysis methods known as "Force Appropriation" or sometimes "Phase Resonance Analysis" which can be used to extract genuine NORMAL mode shapes from measured data obtained from non-proportionally damped systems but these are rarely implemented in commercial modal analysis software and they can be time consuming to carry out.
It is also possible to quantify the degree of non-proportional damping (how much one mode is coupled to another) using an extension of the force appropriation approach. These are relatively new developments however and have yet to take off in a big way (I should know. I was the one who developed them!)
So to respond to your original comment:
"I would be interetsted to read if if people think that these occur due to poor fitting technique, or are fundamental properties of real systems."
