Response Spectrum to PSD?! 4

[TomEME]

Hello, all.

Did a search and found this thread: thread384-106639

My problem is that I am using Solidworks 2008 and it's accompanying Cosmosworks. Now several times a year I get jobs doing seismic analysis for various components at nuclear power plants. The plants typically provide Response Spectrum curves for use as base excitations, as G's vs Hz.

However, Cosmosworks wants PSD values (G^2/Hz vs Hz). I have read that it's not as simple doing the conversion listed in 3rd or 4th post of that thread, and the Miles equation is not usable "in reverse." SW has nothing, and have opened an "enhancement request" for the issue.

Anybody out there have any thoughts on this?

Thanks,

Tom

 

[snoopnoon]

Been a while since I have done this and hope I am not posting bad information here, but you can just do a root mean square analytically. You decide what will be an ok resolution to use for the program and the spec and at each on of those discrete intervals perform RMS calc.

 

[TomEME]

Thanks, snoopoon.

But somehow it seems more complicated than that. There is a paper I found at

http://tinyurl.com/6evc5m

(actually the ASCE website). It talks about Monte Carlo simulations and what not.

Just going by the units, it would seem that, as you say, you take a given point (or interval?), do the rms thing, square it, and divide by the frequency of that point. But in that case, the Zero Period Acceleration values would now decrease with frequency, whereas on a response spectrum curve they are constant above a certain frequency.

For all I know, though, that would be correct. I've just never worked with PSD's in this context (or at all, for that matter).

Thanks again,

Tom

 

[Twoballcane]

In my opinion SRS and PSD are two different animals. It all comes down t the time domain G vs Time. To get a SRS curve your time domain will start excitation and then dampen out where as for PSD the time domain will start excitation and keep going and perhaps create a patter.

However, in your case, I think your applying the wrong application. If they supplied you with a SRS curve, it is a shock load that you have to analyze and not random vibration (PSD). Shock analysis is different than random vibration analysis. So be careful.


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

 

[snoopnoon]

I do not think this is a shock case. But I would be careful when you look at your results that they will be rms results and not Peak response.

 

[Twoballcane]

Just curious, why do you think that? In my experience if I get a response spectrums or shock response spectrum (SRS) it is to mimic the profile on a drop machine or hammer drop machine. In my opinion that’s all its good for. Not sure what else you can get from that. If you are looking for G levels at certain frequencies, than you would have gotten a FFT than a SRS. If you want more meaning they should have given a Pseudo Velocity Spectrum than a SRS.

I guess the OP has to go back and ask for the time domain and see if it is a shock profile (with damping) or random vibration profile (no damping).


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

 

[TomEME]

Actually, the response spectrum in this case represents an earthquake, or more precisely, a curve of points that represent the acceleration (at each frequency) that a single-degree-of-freedom spring-mass-damper system that is resonant at the given frequency, would have to the eartquake. Confusing enough? Trying again, suppose the curve has points from 1 Hz to 20 Hz. The g's of the abscissa represent the responnse of 20 different SDOF resonators tuned to the frequency of the ordinate. Usually several curves are given for various values of damping.

The earthquake form which the response spectrum is made certainly has a time history, and therefore a PSD. But given the phsysical descriptin of the response spectrum that I've shared, it's not immediately apparent to me how to go from response spectrum to PSD.

And I may indeed be using the wrong application. It seems to me someone told me that before, but support for this stuff in Solidworks is a bit sketchy at best.

But still, the paper in my link above purports to be able to make the conversion. I oughta quit being a tightwad and just buy the thing.

Thanks all,

Tom

 

[Twoballcane]

I have to get into some of these earthquake problems some day. In my field energy comes fast (shock) or on going (random vibe).

Good luck!

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

 

[Twoballcane]

Hi Tom,

You got me thinking now, why do they give you a response spectrum instead of a PSD? In your field what do you get out of the response spectrum? What do you determin from that except trying to mimic it on the vib table?

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

 

[TomEME]

Twoballcane,

In a way, that's just what I'm trying to do. I put an FEA model on a "virtual vib table," apply the reasponse spectrum as input base excitations, and see if something bad happens.

BTW, that's an interesting handle you have. Sounds like a character from Genesis.

Tom

 

[fetraining]

TomEME,

This is a long reply – but the topic is complicated!
The bottom line is I don’t know a way of taking an SRS input curve and turning it into a PSD input curve. In many industries structures have to be qualified by analysis against both an SRS loading specification, and a PSD curve specification. The analyses are different and carried out completely separately, except from maybe re-using the normal modes in both.

You have neatly described the analysis method to get an SRS response to an SRS input. The input curve is g versus Hz. The process is just to find the natural frequencies of the structure and then look up the corresponding input g level. Knowing the damping level we can get the peak response at each of those frequencies. There is a little bit of black magic to figure out how peaks are combined across frequencies – does all of the structure respond with maximum amplitude at all of its natural frequencies, or do we use a less conservative method. But other than that it is a clear cause and effect.

The PSD input is based on a random simulation of the applied loading, rather than the deterministic SRS loading. The subsequent analysis calculates a random response.

The input is g^2/Hz versus Hz. Unlike the SRS curve you can’t really look at a point on a PSD curve and say what level of acceleration that represents at the particular frequency. The key is to look at the whole curve;
If you take the area under the curve it is g^2/Hz * Hz ==> g^2. The single number represents the square of the input acceleration.
If you take the square root you get back to a g value. This is the famous RMS g – Root Mean Square g. The RMS g is the input or output g level the structure will see during 68.3% of the loading spectrum. It is also equivalent to one standard deviation ‘one sigma’. Most designs are done to three sigma ; which means we multiply g by 3.0 and then the chances of seeing that level of loading or response are 99.73% Chance of exceedence is 0.275%.

The link you referenced is a neat way of getting approximate amplitude for an equivalent deterministic sine response to a PSD input. It is in two parts. The first part uses Miles equation to get an equivalent static g from a PSD response. The second part turns this static g into an oscillating g. The first part using Miles equation makes two big assumptions; the response is dominated by a single strong mode and the PSD input curve is a constant g^2/Hz. This is great for very simple structures that you can equivalence to a few DOF, or to do quick checks on order of magnitude in parts of the structure that may show clear dominant modes. It is not feasible for an overall approach. The structural response and the input PSD are too complicated.

An SRS analysis is very straightforward and most FE solvers have it as a spin off to a normal modes analysis. You don’t need to apply base motion or change the boundary conditions from a normal modes analysis.

A PSD analysis is usually in three phases; calculate the natural frequencies ( normal modes), calculate the frequency response to an input motion or force, apply the PSD input to the frequency response to get the PSD response and finally calculate RMS responses from the PSD response curves.

I checked the COSMOSWORKS website and it seemed that both types of analysis were available.
References for Random analysis I use are:
D.S. Steinberg – Vibration Analysis for Electronic Equipment, Wiley 2000
P. H Wirsching – Random vibrations, Theory and Practice Wiley 1995
Don’t be put off by the title in the first one. It applies to most structures.

I hope this helps,

Regards Tony


Tony Abbey

http://www.fetraining.com

 

[TomEME]

Tony,

Thanks so much for a valuable post. Fortunately, I was able to understand it!

I had hopes that indeed the conversion would work (plus spent 30 bucks & too much valuable time on that paper). Mainly because after years of using WECAN (red-headed stepchild of ANSYS) we switched to COSMOS - and I must be getting cranky & old, because I despise the GeoStar interface needed to do a proper Response Spectrum. If you are familiar with the ANSYS input deck (well-commented and formatted in columns) the GeoStar deck & input method is just tough for me to swallow.

But yes, I was aware that the GeoStar option, with all the various combination methods, was there. I just didn't want to bite the bullet and do it.

Thanks again,

Tom

 

[Twoballcane]

Tony,

Nice job, but what are your thoughts on how to tackel it? As a shock problem or random vib problem? My thoughts are since the spec came in as a SRS it is a shock study. So you have to start calculating the shock amplification at frequency and so on. Just my 2 cents.

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

 

[fetraining]

TomEME,

I thought about it some more and read the abstract of the reference paper more carefully. It seems there may be a route through this, but I don't know what the assumptions are behind it. I think that most certification authorities would view it as a bit radical to do a random analysis when they are expecting an SRS solution to a Seismic analysis. Worst case scenario is you would have to justify it and lead them through the hoops as well!

There are some relevant papers on this site:

http://www.vibrationdata.com.

I think the author posts here and he is very helpful indeed in my experience.

Twoballcane:

I think the conclusion is to do it as the shock problem it was intended to be. Sorry to hear GeoStar is a pain Tom. Anyone for Nastran?

regards,

Tony




Tony Abbey

http://www.fetraining.com

 

[TomEME]

We were looking at the FEMAP/Nastran route as well as ANSYS when we finally ended up with Solidworks/COSMOS. Either were more expensive. I liked the FEMAP interface, but then again, that wasn't for the full-blown NASTRAN.

I think the boss's view was that all of 'em can do garden- variety linear FEA well enough, which is what most of our FEA work is. Therefore, you go cheap (and with a package our youngest guys had trained on in college) and just jump through the hoops on the occasions tha you need to.

But yeah, spending other people's money, I'd have taken NASTRAN or ANSYS any day. I've been at these things since puch card days and I have my preferences (i.e I'm an old grump).

Thanks again, Tony, I'll check out that site!

Tom

 

[tomirvine]

A time history can be synthesized to satisfy a shock response spectrum. (The time history will not be unique.)

Then you can perform a modal transient in FEA.

Tom Irvine

http://www.vibrationdata.com

 

[Tunalover]

Tom Irvine-
Are you saying that a time history can generate an SRS but the reverse is not true; that is, the SRS cannot give back the exact time history response it was created from?


Tunalover

 

[cbrn]

Hi,
Tunalover, I think it's so. In fact, you can Fourier-trnsform a time-history in order to get an amplitude spectrum AND a phase spectrum. In order to be able to do the reverse, both informations must be available. Generally, however, earthquake spectra are only expressing accelerations versus frequency, so the amplitude data is here, but there is nothing about phase. So you have to "guess" which phase distribution will cause the structure's response to be the worst: uniform (constant, i.e. null) phase? Random phase? And so on...

Regards