A question was asked of me if there could be harmonics derived from a resonant frequency (not the forcing frequency, just the resonant frequency). I don't see what would modulate the frequency, and couldn't answer in an intelligible, understandable way.
Some one enlighten me.

Dave

I am not sure I understand the question, but it is possible for a second mode to have a natural frequency that is precisely twice the frequency of the first mode. An example is a guitar string.

In this case a impact event (like plucking a guitar string) would excite both modes... It would not be a modulation, but rather the excitation of two frequencies.

Steve,

I couldn't answer intelligeably, nor could I ask the question LOL I'll try to do better. It's been a long and hot day.

I really mean if I excite a resonance, can there be harmonics of that resonance frequency. I understand the concept of the guitar string, but can I develop resonance harmonics similiar to the harmonics from a classic "type C" looseness?

Dave

I have not experienced this personaly but what I have been told by more than one instructor in training classess is that if a peak has an exact multiple ( or harmonic ) that it is not a resonance.Wheather that is true or not I don't know. I haven't encountered that situation.

Mike

Steve from Malaysia mentions a well studied example. This does have some differences from many mechanical natural frequencies (and similarities, too). Strings like this seem to depend upon tension and mass distribution.

Given than my genetic makeup did not provide rhythm, I might pluck a string and not get harmonics, at le4ast not pleasant ones.

Other mechanical structures may have exact multiples, but given an actual manufactured piece the probability of an exact (as in mathematically) harmonic would probably be zero.

Some structures have repeated roots, two or more natural frequencies at the same frequency. Cylinders and disks can do this, but again in the real structure, the exactness will probably be an almost.

At resonance harmonics can be often seen. As noted above by Dave, this most often does not relate to multiple resonances being excited. Non-linearities explain this. Also, forces may not be sinusoidal.

I have played guitar for about 30 years Bill and I still occasionally pluck a string and get unpleasent harmonics...

BTW I am still trying to get moved... Should be in KL by September.

Bill - Could you provide some more detail on how non-linearity or non-sinusoidal forces can produce harmonics at resonance?

Is there a "simple" non-linear model that could display this behavior? I'm thinking there would have to be an analytical solution to the partial differential equations to get exact harmonics, but I wouldn't be suprised if I'm wrong.

Non-sinusoidal forcing functions may have a 2X or other harmonic content. This will force a linear system. Resonance need not be involved.

Example: Say your spring has a square law, like the negative spring of a motor magnetics. Given a displacement (small displacements may cause the spring to react mostly as a linear spring - Taylor series stuff or just expand the square terms and compare size). Introduce a sinusoidal displacement (largest at resonance). The spring reaction force to the A * sin(x) is K * A^2 * sin^2(x) which by trigonometry is K*A^2 *(1-cos(2x))/2 - The 2X will come out of that.
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A shaft asymmetry has a harmonically varying shaft stiffness (and/or inertia). This is a parametrically varying system - Harmonics can result as well as instabilities (Although for this particular example I have yet to meet anyone that has seen it in the field.