Response spectrum 1

[mech2926]

Hi,
I have a question on response spectra. I have attached a figure showing an arbitrary response spectrum. Assume that my component's first mode is at the vertical red line. If I assume that all the mass is participating in that mode, and apply the acceleration (in my Nastran model) shown by the horizontal red line, is that conservative?

My thinking is that regardless of what other modes the item has, it should never see an acceleration higher than the horizontal red line. But I'm not completely sure and would really like someone to either confirm this or tell me I'm wrong.

Thanks!

 

[IRstuff]

Why is that the case? If you apply 5x that frequency, why wouldn't the component see it?

TTFN

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[mech2926]

IRstuff,
I'm not sure I understand your question. I'm coming from the perspective of using a static analysis rather than a response spectrum analysis. That's why I wanted to make sure that the approach I mentioned was conservative; if it's not then I need to find another way, or add some fudge factor to ensure I get a conservative acceleration.

I know that if my system has only one mode (a single degree of freedom system), then it will see the acceleration on the response spectrum curve that corresponds to its modal frequency. I'm less clear on multi-mode (real) systems, because if you have multiple modes you could end up with an acceleration higher than the curve. I guess I could rephrase my question to be something like: If the lowest mode of my system is at the vertical red line, can I obtain an acceleration value that would enable me to analyze it statically and conservatively?

 

[GregLocock]

I must admit I am having trouble following your reasoning, but no is the answer to your question. For instance, in your example, the peak value is of more interest than the red line. But you can't even use that for fatigue analysis, conservatively.





Cheers

Greg Locock


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[TERIO]

I would argue that you are conservative. In a response spectrum analysis you are finding the peak response of each mode, but don't have any information about when those peaks occur relative to each other in time. The worst case would be the peak response of each mode being at the same time in the same direction, in which case the total response would just be the sum of all the peak response. Essentially your method assumes this and shifts the spectrum at frequencies higher than the vertical red line up to the acceleration level at the horizontal red line. This is similar to doing a "missing mass" correction to account for all the modes you have not calculated.

NRC Reg Guide 1.92 has some discussion and a good list of references on response spectrum analysis if you need it.

I'm not sure I understand Greg's concern on fatigue. The performing a response spectrum just gives you the stresses; an appropriate number of cycles for your loading would need to be considered.

 

[mech2926]

TERIO,
Thank you, that definitely helps. A lot of the math in the NRC document is over my head (I have only a humble bachelor's degree), but I'll see what I can learn from it. Maybe you can clarify something that has been bothering me for a while and is related to this subject. One of the methods I know of for seismic analysis is to take the peak of the response spectrum and multiply by 1.5, then apply this acceleration statically to the model. What is the basis for the 1.5? If all the mass of the structure participated in a mode at the peak, then the peak would be the actual acceleration. Is this related to the possibility of closely spaced modes? Can you actually have an acceleration greater than the peak?

Thanks again

 

[GregLocock]

What on Earth has seismic modelling got to do with fatigue analysis?

Cheers

Greg Locock


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[TERIO]

mech2926,

That 1.5 number sounds familiar to me as well but I'm not sure of the basis, perhaps I'm missing something as well. I'll have look around a see if I have something on it.

The closely-spaced modes problem relates to not knowing when the peak responses of modes occur in time. Modes that are at nearly the same frequency tend to peak near the same point in time and the combination of the response of each mode should reflect this.

Greg,

It doesn't really have anything to do with fatigue and hence my confusion. Perhaps we are talking about two different things with similar names. In the language I'm used to a response spectrum is a plot of the peak response of SDOF oscillators to a given input motion. A response spectrum analysis uses that info to approximate the peak response of an MDOF system to that input.

 

[GregLocock]

Ah I see, we aren't talking about fatigue, that was my fault.

My guess is that that is an excitation spectrum (ie what is applied at the foundation). Then the Op's post makes a glimmering of sense.

Well I still think that ignoring the enormous low frequency peak in that response spectrum is non conservative. So my answer is still no, it is non conservative, for general systems.

If your system has sufficiently low damping then the stress spectrum may be dominated by the response at resonance, but it may not be. How can that be a conservative conclusion?



Cheers

Greg Locock


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[TERIO]

Regarding the first point I think the OP is saying that he has calculated or somehow shown that his lowest frequency mode is at the vertical red line in his plot, so his system won't see the peak at lower frequency.

In my experience response spectrum is used for short duration random loading (e.g., seismic excitation), where I would think resonance is less of a concern because you aren't driving it at a constant frequency like you may in a more typical mechanical vibration problem.

 

[GregLocock]

Here's a simple (but at least analystical) model of a tyre running down a road. Its resonance is at 11 Hz. The input spectrum is pink noise, commonly found in nature.

The response is dominated by the non resonant low frequency stuff, NOT the response at resonance.





Cheers

Greg Locock


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[mech2926]

If the system's modes are in the flat part on the right end of the response spectrum, then I think they are above the forcing frequencies. I think that the magnitude of the spectrum on the right end is equal to the peak input acceleration (the acceleration of the ground). Since the system would be "stiff" compared with the forcing function, nothing would be amplified and the system would simply experience the acceleration level at the right end of the spectrum.

My issue has to do with a system that is not quite at the "flat part," and will therefore experience some amplification. It would make sense to me that it would be conservative to just apply the value on the curve. However, I wonder whether several other modes nearby could make the actual response higher than the curve.

The reason for my doubt is the "static coefficient method," which is discussed in IEEE-344 (seismic qualification) and is quoted in many places on the internet. This method takes the peak of the curve and multiplies it by 1.5 to account for "the combined effects of multifrequency excitation and multimode response." I'm not sure what that means, and it is generally assumed that the system "can be represented by a simple model" and is "physically similar to beams and columns." The whole point of the static coefficient method is that you don't have to know the modes of the system.

This just occurred to me: could this factor (1.5) be due to the fact that the system could have multiple modes that act in different directions? Let's say I have 2 columns with a horizontal beam in between: the two columns could be excited out-of-phase with each other, which would increase the stress in the horizontal beam. You would not get this same effect if you applied a static acceleration. Perhaps that is where the 1.5 comes from?

 

[TERIO]

Take a look at the section "Equivalent Static" in this paper.

http://www.iasmirt.org/iasmirt-2/SMiRT19/S19_FinalPapers/K13_5.pdf

It says that taking the peak value of the spectrum (i.e., factor of 1.0) can "usually be shown to give conservative results" and references an older paper by the author (which I have not found). This particular paper doesn't happen to point out the unusual case where it would not be conservative.

 

[TERIO]

Another study on equivalent static factors:

http://www.iasmirt.org/iasmirt-2/SMiRT19/S19_FinalPapers/K08_2.pdf

 

[hacksaw]

have to agree with Greg on this discussion,

what is unclear is that you are tossing out an "arbitrary reponse spectra" that does not show the modes of concern.


what you've shown appears to be the excitation spectra, although the shape of the curve appears to suggest that non-linear structural effects may be present

all vibration analysis and testing of the system response always exhibits the presence of the structual modes, they are not invisible to such tests unless you happen to place the sensor at one of the nodes.

if indeed your "arbitrary spectra" is that of the excitation, and your red lines indicate the lowest system mode, then you are actually exciting those modes albeit with reduced intensity, however, the system response to that is governed by any damping present.

fatigue issues are another matter. to have a discussion in that regard you need far more specifics that you've provided

 

[mech2926]

hacksaw,

I'm not familiar with "excitation spectra"--is that a graph of the input acceleration (what would be the floor motion in my case)?

What I have is a response spectrum, which is the response of a spring-mass-damper mounted to the floor (the x-axis represents the frequency of the spring-mass-damper). The spectrum I posted is one I drew by hand in Microsoft Paint, but it illustrates the basic pattern of all the ones I've seen: low accelerations at low frequencies, a peak in the middle, and then sloping down to a flat line (the ZPA) on the right.

I just want to make sure we're talking about the same thing.

 

[hacksaw]

mech2926,

that is what was meant regarding excitation spectra,

for the response spectra, the peak you've drawn is the system resonance assuming a swept frequency excitation.

The vertical red-line is where you predicted the resonance to occur. you'll have to sort out why it does not, and that is where actual details of the measurement are critical, amplitude, frequency, etc.

the "shape" of your resonance curve, suggests frequency dependent effects beyond simple spring-mass resonance, and may depend on the amplitude of the excitation.

 

[TERIO]

hacksaw,

I think you are talking about something slightly different. A response spectrum is not the response of one system to excitation at many frequencies. It is the peak response of many systems to a given base input motion (e.g., a time-history record of an earthquake). A response spectrum for a given base input motion would be generated as follows:

1. Choose a certain damping level, say 5% of critical.
2. Solve the time history response of an SDOF system with natural frequency, f, and damping 5%.
3. Take the maximum acceleration (absolute value) of the solution from step 2 and plot the maximum acceleration vs. the natural frequency, f, as one point on the response spectrum curve.
4. Repeat steps 2 and 3 for many frequencies, plotting the maximum acceleration vs natural frequency points to build the response spectrum curve.

 

[hacksaw]

the query involves frequency spectra without details (part of the problem).

the spectra that i'm familiar with consists of shaker table, impulse testing, broad-band noise where the source consists of its own statistical description), and analysis of time-series data.

my appologies but I am not seeing a match between my own experience, such as it is, and the frequency spectra put forward initially.

how do you explain what appears to be a frequency dependent damping term in the indicated spectra?

 

[TERIO]

My experience with response spectra has been for seismic analysis and the spectra drawn by the OP is qualitatively like those I have seen. The input signal is random, but not uniformly random in a white noise sense. It has more energy content at some frequencies than others.