×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Positive crossings

Positive crossings

Positive crossings

(OP)
Can anyone tell me the difference between positive crossings, positive crossing rate and frequency of positive crossings. This different terms are used in different text (I'm talking about random vibration) I am specifically referring to books by Newland, "random Vibration and Spectral analysis", Wirsching, Paez and Ortiz "Random Vibrations, Theory and Practice", J. D. Robson, "An introduction to Random Vibration"

Is there anyone familiar with this?

Thanks

RE: Positive crossings

izax1:

I believe they are all the same.  I have heard all three terms used interchangeably.  Typically, they are used in fatigue analysis or determination. People in our lab typically perform sinusoidal vibration to obtain the first three most prominent resonant frequencies (fn) and transmissibilities (Q). These are typically the frequencies with the highest transmissibilities.  Then people in the lab perform random vibration tests but always calculate the "Zero Positive Crossings" first.
SINUSOIDAL TESTING
Get fn(1-3) and Q(1-3).  The number of fatigue cycles accumulated during a resonant dwell of a sinusoidal test is (resonant frequency x dwell time).
RANDOM TESTING
The number of fatigue cycles in a random test is harder to calculate.  The number of fatigue cycles must relate to the frequencies that do the most damage, however, all of the exciting frequencies are present at once.  
S. O. Rice,"Mathematical Analysis of Random Noise",pp. 353-461, offers a great explanation of zero crossings both + and -. It is defined in terms of per unit time or a rate, so the units are Hz.  (Integration based equation.)

D. Stienberg,"Vibration Analysis For Electronic Equipment," further defines a positive zero crossing.  The number of POSITIVE ZERO CROSSINGS (N0+), is the number of times, on average that the displacement trace crosses the zero axis with a positive slope.  

For lightly damped structures with several resonant peaks, D. Stienberg offers a relatively simple theoretical equation that our lab uses.  It is based on the assumption that each resonant peak acts as a single degree of freedom.  On lightly damped structures we have used it with some success.

N0+=(1/(2 x pi))x (SQRT(numerator/denominator))  Hz
numerator:(a/b + c/d + e/f)
a:(pi/2)x(PSD @ fn1)x Q1
b:[(2 x pi) x (fn1)]^2
c:(pi/2)x(PSD @ fn2)x Q2
d:[(2 x pi) x (fn2)]^2
e:(pi/2)x(PSD @ fn3)x Q3
f:[(2 x pi) x (fn3)]^2
denominator:(g/h + i/j + k/l)
g:(pi/2)x(PSD @ fn1)x Q1
h:[(2 x pi) x (fn1)]^4
i:(pi/2)x(PSD @ fn2)x Q2
j:[(2 x pi) x (fn2)]^4
k:(pi/2)x(PSD @ fn3)x Q3
l:[(2 x pi) x (fn3)]^4

D. Stienberg EXAMPLE
IF:
fn1:138 Q: 5.0
fn2:279 Q:17.0
fn3:534 Q:4.0
THEN:
N0+ = 196 Hz

Further note that there are more peaks than Zero Positive Crossings.  Why? The displacement will sometimes reverse before crossing the zero axis.

Finally, The +zero question was posed to T. Paez during a "Random Vibrations" course(1998) involving the text you have mentioned above.  As I recall, he agreed with the explanation.

Hope this helps!
Kaiserman

RE: Positive crossings

(OP)
Thanks Kaiserman

I will look into Steinbergs book.

Izax1

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources