effect of force on resonant frequency

[Tmoose]

The December issue of "Electrical Apparatus" has an article on motor ventilating fan design. One statement on page 24 is that the steady force from wind pressure (which might be "as great as the weight of the blade itself") has the effect of reducing the blade's resonant frequency.

I think that the force is being mistaken as interchangeable with blade mass. That is easy to do, since resonant frequency formulas and tables often are related to static deflection, which does depend on force.
I worked with a very useful shaft analysis program from a big bearing company in the 90s that allowed force inputs but carried the results calculation beyond deflection and to First bending mode resonant frequency. The instruction manual warned about the incorrect wn result, but I knew at least one user that was unaware of the distinction.

Dan T

 

[izax1]

I haven´t read all the posts here, but I think you are discussing stress stiffening. And stress stiffening is absolutely vital when calculating Natural frequencies of a turbine engine. Try measuring the natural frequency (in bending) of a turbine blade at 0 rpm compared to a turbine blade at 5000rpm

So, electricpete based on the above, I do not agree to your post from Dec 12 that:"Linear system resonant frequency is not affected by any static force." Of course it depends on how you define "linear system" and "static force", but turbine blades will have higher bending frequencies at high rpms, which again are lowered due to the material softening at higher temperatures.

 

[electricpete]

So, electricpete based on the above, I do not agree to your post from Dec 12 that:"Linear system resonant frequency is not affected by any static force." Of course it depends on how you define "linear system" and "static force

You mentioned the definition, so I will look for the most common definition I can find. If you type “linear system” into google, the very first thing that comes up is from Wikipedia:

http://en.wikipedia.org/wiki/Linear_system

Scaling, addition and time-shifting of the input results in similar scaling, addition and time shifting of associated outputs...... Linear systems satisfy the properties of superposition and scaling or homogeneity

Let use say we have an input Force1(t) at frequency f1.
Let us say we have another input Force0(t) at frequency of zero (static = dc).

The steady state response to Force1(t) will be called y1(t), and it will be at frequency f1.
The steady state response to Force0(t) will be called y0(t), and it will be at frequency 0

By superposition (which applies to linear systems as defined above), the steady-state response to the combination of Force1(t) and Force0(t) is the sum of the individual responses, which is a response of y1(t) + y0(t).

Note that the time-varying portion of the combined response remains y1(t). i.e. the dc force did not affect the response at frequency 1.

If you want to suggest another definition for linear, that’s perfectly fine with me. What I wrote is also correct, as just explained using a very common accepted definition of “linear system”.

I have provided analysis above (13 Dec 11 10:11) that for the max reasonable axial loading (corresponding to 30 kpsi compressive or tensile stress), the change in resonant frequency will be less than 1% if L/D is less than 10. This leads me to believe it would be negligible for most run-of-the-mill industrial motor/fan shaft applications (lets say at/below 200hp and in the speed range 1200 - 3600rpm). Feel free to comment if that doesn’t sound right. As L/D of the object increases above 10 (more like turbine flexible turbine blades), then the change in resonant frequency for that loading level becomes more significant.


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(2B)+(2B)' ?