resonance frequencies and harmonics
resonance frequencies and harmonics
(OP)
Hello,
if a system has got a basic resonance frequency, it's also supposed to swing in the harmonic frequencies, belonging to the basic resonance frequency, if excited, and these harmonic frequencies are supposed to be whole-number multiples of the first frequency(for example: 2..4..8...12...etc.)?
Should FEM simulations with nonlinear geometry also yield whole-number-multiples of eigenfrequencies? In my calculations the multiples don't seem to be whole-numbers.
if a system has got a basic resonance frequency, it's also supposed to swing in the harmonic frequencies, belonging to the basic resonance frequency, if excited, and these harmonic frequencies are supposed to be whole-number multiples of the first frequency(for example: 2..4..8...12...etc.)?
Should FEM simulations with nonlinear geometry also yield whole-number-multiples of eigenfrequencies? In my calculations the multiples don't seem to be whole-numbers.





RE: resonance frequencies and harmonics
The moment you included the mass and shape factor in the analytical model, you have introduced part of the reality and you will never get the integer multiples you are looking for. Also part of the problem is that FEA is an approximation and not exact. You will always have calculation residuals in each of the matrix calculation resulting in variation between harmonics multiple.
Have fun
RE: resonance frequencies and harmonics
Here is my response, starting from scratch: For simple beam geometries, it sometimes works out that the higher order modes are exact integer order multiples of fundamental. For example simply supported beam. If fundamental mode is at frequency f1, the higher order modes occur at frequencies fk = k^2*f1 where k = 2, 3, 4 etc..
For typical real-world geometries, the higher modes do NOT occur as exact multiples of the fundamental frequency.
Separate, DIFFERENT subject, if you have non-sinusoidal periodic excitation (for example square wave) at fundamental frequency of f1, the signal will contain content at exact integer multiples of the fundamental.
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(2B)+(2B)' ?
RE: resonance frequencies and harmonics
fk = k * f1
Eignevalues would step in squares-of-integers, but the freq's. are sqrt(eigenvalues).
That said, I can think of few real-world structures that show such simple behavior. Pipe organ oscillations, some simple torsion systesm, maybe. But even a cantilever beam has frequencies that scale by non-integer values, and real world objects that can vibrate in 3 axes and have combined modes involving all those axes just aren't gonna follow anybody's rules.
RE: resonance frequencies and harmonics
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(2B)+(2B)' ?
RE: resonance frequencies and harmonics
RE: resonance frequencies and harmonics
All responders agree these types of integer-multiple patterns only occur in extremely simple problems, which is not likely in a problem complicated enough to be solved by FE method.
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(2B)+(2B)' ?
RE: resonance frequencies and harmonics
Good grief. SDOF has one resonance, by definition. I can't say i agree with much of the rest of that post except in the most general handwavy terms.
There are comapraitively few multi-dof systems that obey a strict integer (k*f1) harmonic series for their frequencies. Plucked taut strings, and organ pipes, and presumably some other 'transmission line' like systems do.
Cheers
Greg Locock
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RE: resonance frequencies and harmonics
- Steve
RE: resonance frequencies and harmonics
RE: resonance frequencies and harmonics
RE: resonance frequencies and harmonics
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(2B)+(2B)' ?
RE: resonance frequencies and harmonics
So I don't get too hoity toity about that.
In the real world lab tests we often see much cleaner transfer functions from a swept sine modal test rather than random input, partly because the system is only being excited at the force level for each frequency.
Of course if you don't call them resonances, all you have to do is invent another word for them.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: resonance frequencies and harmonics
RE: resonance frequencies and harmonics
RE: resonance frequencies and harmonics
Did you mean to say "resonances" rather than "harmonics"
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(2B)+(2B)' ?
RE: resonance frequencies and harmonics
If you are inputing a high amplitude single frequency and driving a system to its bump stops, you'll measure a squared-off response. That will naturally have harmonics of the driving frequency. People get obesessed trying to find the source of these additional frequencies. Somethimes you just need to go back to the time domain to understand a system.
- Steve
RE: resonance frequencies and harmonics
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(2B)+(2B)' ?
RE: resonance frequencies and harmonics
Likewise, a linear system cannot generate harmonics, therefore, only a nonlinear system can.
TTFN
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RE: resonance frequencies and harmonics
M
--
Dr Michael F Platten
RE: resonance frequencies and harmonics
H(w) = Output(w)/Input(w) may be very large at resonance (w=w_resonant), but it's a constant (in the sense that it doesn't change over time and doesn't depend on magnitude of the input).
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(2B)+(2B)' ?
RE: resonance frequencies and harmonics
RE: resonance frequencies and harmonics
I agree with FE.
The frequencies present on output of non-linear system do not necessarily match those present on input. And in particular it is not uncommmon for sinusoidal input to result in output which includes harmonics of the input frequency (for example sinusoidal unbalance force causes harmonics of running speed in vibration spectrum).
Note, this is different than having resonant frequencies which occur in exact multiples of the first resonant frequency.
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(2B)+(2B)' ?
RE: resonance frequencies and harmonics
(for example sinusoidal unbalance force in presence of looseness, which is a non-linearity) causes harmonics of running speed in vibration spectrum).
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(2B)+(2B)' ?
RE: resonance frequencies and harmonics