What is Pseudo Velocity? 2

[Twoballcane]

Hi guys and gals,

I was looking at a shock requirement and the chart is in pseudo velocity (fps Yaxis) Vs Hz (Xaxis). In the upper right hand corner there is relative displacement (Xaxis) Vs acceleration (Yaxis). How should I read this and more importantly, what should I walk way with after reading this?

Any comments would be welcomed.

Thanks for your effort in advance.

Tobalcane

 

[MikeHalloran]

One of us may be remembering something wrong, and often enough it's me, but here's what comes out of the old memory bank:

The displacement, acceleration, and velocity are real enough. The _frequency_ is fictitious, because in shock there's only one explosion or impact or other forcing function. However, modeling it as a sinusoid makes the math easier.



Mike Halloran
Pembroke Pines, FL, USA

 

[IRstuff]

Any shock shape can be FFT'd into a frequency spectrum. The latest rage is the Shock Response Spectrum (SRS) approach. Mil-Std-810 shock section has a description about this.

see also:

http://www.vibrationdata.com/tutorials.htm

in particular:

http://www.vibrationdata.com/SRS.htm

TTFN

 

[tomirvine]

Thanks to IRstuff for mentioning my site. Please also visit:

http://www.vibrationdata.com/QE.htm

The Shock Response Spectrum (SRS) models the peak response of a single-degree-of-freedom (SDOF) system to a base acceleration, where the system's natural frequency is an independent variable.

The absolute acceleration and the relative displacement of the SDOF system can be readily calculated.

The absolute velocity, however, is more difficult to calculate accurately.

The "psuedo velocity" is an approximation of the absolute velocity.

The peak psuedo velocity is equal to the peak relative displacement multiplied by the natural frequency "omega sub n" which has units of radians per second.

Tom Irvine

 

[Twoballcane]

Thanks guys and especially to Tom…

 

[Twoballcane]

Hi guys / gals,

Sorry for dragging this out of the grave, but now I had some more time to work with this profile, I have some more questions.

If I had break points as follows (on 4pt log paper):

Frequency (Hz) Pseudo Velocity (fps) (PV)
2 16
3 25
6 25
250 0.6

1) At freq and PV of 2 and 16 I get a relative displacement of 15 inches. Does this make sense? What does this mean?
2) I have read that the relationship of the PV to stress is
Stress = density * (youngs mod / density)^.5 * velocity. Does anybody use this equation?
3) If I have Fn higher than 250 Hz do I still use the PV curves?
4) What is the difference between Pseudo Velocity and Relative Velocity?
5) Do you use PV profiles more than SRS (G vs Freq) curves? Is the trend going to use PV profiles instead of SRS profiles?

I would be very grateful for any comments.

Thank you in advance…


Tobalcane
"If you avoid failure, you also avoid success."

 

[IRstuff]

These should be based on sinusoidal motion, so a 2 Hz sinewave with a peak velocity of 16 fps will have an antiderivative, which is the displacement curve, with an amplitude of 15.27 inches.

TTFN

 

[Twoballcane]

Hi IRstuff!

Thanks for responding, I am so confused with this profile. Are you telling me that the plate will displace 15.27 inches? We did a 15G .040 sec pulse and overlap this with the PV profile and at 2Hz I am getting an 8 inch displacement. I don’t think my plat can even displace 8 inches. So I am really missing something here.

When you took the antiderivative (or integral) did you find the area under the PV vs Feq curve?

Also, have you ever used stress = density*(youngs mod/density)^.5*velocity?


Tobalcane
"If you avoid failure, you also avoid success."

 

[IRstuff]

start with amp*sin(2pi*f*t)

derivative is amp*2*pi*f*cos(2*pi*f*t)

max velocity is therefore amp*2*pi*f, solcing for amp = maxv/(2*pi*f) gives you 15.3-in amplitude.

However, that's applicable if you have only that one frequency running.

A random profile is simply a random generation of frequencies without any steady state. Therefore, the amplitude of a random profile can only be related to the total rms energy. That's why it's a psuedo-velocity, based on the power spectral density of the profile.

What it means is that IF you dwelled at that frequency with that psuedo-velocity, you'd need a 15.3 in displacement to get there.

TTFN

 

[Twoballcane]

Thank you IRstuff, I’m kind of seeing the light. So is pseudo velocity per SDOF and relative velocity the average or over all velocity?

Since I’m asking, do you know of any good references (a book perhaps) that you can point me to? I have googled and got some white papers, but it all looks conflicting. That is where I got the stress equation, but the units don’t work out.


Tobalcane
"If you avoid failure, you also avoid success."

 

[IRstuff]

I've finally made some sense of your original post. Those types of grpahs are peculiar to Navy shock and vibration, e.g., MIL-STD-167 and MIL-S-901D. The basic (mis)information is that the axes only apply to sinusoidal excitations, hence the prefix "psuedo." The psuedo-velocity is what the velocity would be if you had a sinusoidal excitation of that frequency with hypothetical amplitude based on the integration of the sinewave velocity.

If you can find it, the July 14, 1972 NRL Report 7396, "Shipboard Shock and Navy Devices for its Simulation," by E.W. Clements, is the reference material for MIL-S-901D. There's some good tutorial material in the front, discussing plotting various shock profiles on 4-coordinate graphs. It's hypothetically available from the National Technical Information Service, but my hard copy was gotten years ago, so I don't know if it's still available.

If this is the sort of thing you're looking at then the only thing you can take from these graphs is that it's comparable to the Fourier transform of the input stimulus, be it the actual shock pulse or the random vibration background.

TTFN

 

[Twoballcane]

IRstuff if I can give you more stars I would. This is a Navy shock that I am trying to understand and then apply it to our design. A 15G @ .040 sec shock pulse is close to the PV curve. 15G @ .040 sec pulse makes sense to me. I can make sure that I can keep at lest on octave away from the forced response and also calc my shock amplifications. I think I will go forward with the 15G shock pulse.

IRstuff, thank you very much for your help.


Tobalcane
"If you avoid failure, you also avoid success."