Damage from modal amplificaiton of stress

[vorwald]

I have a metal structure that consists of webs and caps (beams). I also have a detailed NASTRAN model. The structure is subjected to periodic loading (17.5 Hz). The load consists of large amplitude, short duration pulses. I have data from 28 strain gauges throughout the operating conditions. The measured strains are not large enough to cause any fatigue damage. However, the strain response shows a damped, free decay between 180 to 400 Hz, depending on the location. 180 Hz corresponds to the 17th NASTRAN mode.

I am concerned that high frequency structural modes are being excited by the applied loading. From NASTRAN, we calculated the maximum modal strain divided by the strain the gauge location to estimate a modal amplification factor. These factor are all large than 10. If I scale the measured strains by 10, the resulting fatigue life is unacceptable. Most of the NASTRAN estimated modal amplifications are quite a bit larger than 10.

At this point, I have identified a potential risk of premature failure resulting from excitation of structural modes. I am not sure what should be done next. Things that can be done include the following.

a) Refine the risk assessment with addition inspection of the existing data. This would consist of using the coherence between the gauges to identify which gauges are participating in the modal response. Then calculate the amplification factor between the participating gauges. Compare these amplification factors with NASTRAN amplification factors for each gauge to identify which NASTRAN mode(s) are possibly being excited. Estimating the mode shape should allow better estimate of the risk.

b) Refine the risk assessment by conducting additional tests. Add accelerometers to measure the deflection under loading, and extract out the mode shape. Once the mode shape is known, identify the areas of highest stress, and put strain gauges there.

c) Start the design process of a device to absorb the high frequency energy.

I'm more of the mind to forget about further estimation of the risk since it is clearly a high mode that is being excited. If there is a high frequency structural mode being excited the mode will be fairly convoluted, and will have high stress concentrations somewhere. However, it is possible that it is a local mode (of the nearby web/cap/stiffeners) that is being excited, which may not have large stress concentrations elsewhere.

Has anyone had previous experience with estimating the fatigue damage from low frequency forcing exciting high frequency modes.

Any advice, suggestions, prayers are appreciated.

 

[GregLocock]

In a linear system you can't excite high frequency modes with a (pure) low frequency input.

Therefore either you input force has some high frequency content (typically due to the way that it starts or stops) or your system is non linear, or there is some other issue.

I like a and b out of your choices, in the first instance. Is your drive signal representative of the in-service loads, or is it likely that the in-service loads do not have any high frequency content?

My gut feeling is that I would ignore a 180 Hz fatigue 'problem' on a car body, but not on an engine. That is, the likely input frequencies in service would help me to decide what to do.

Incidentally I have a very hard time believing in the accuracy of the 17th mode of any Nastran run, particularly since you have not done an experimental modal analysis to correlate it.



Cheers

Greg Locock

 

[vorwald]

Greg

You touched on a number of key points. The low frequency forcing is not sinusoidal, but consists of large amplitude pulses, and therefore has a lot of high frequency sinusoidual content in it.

The test conditions replicate field service, so the drive (forcing) should be the same. From what I can see, the high frequency forcing will be there; it comes from the impulse nature of the loading.

The gut feeling issue is bothering me also. I live in the world of frequencies between 3 Hz and 30 Hz. 180 to 400 structural modes is hard to believe. But the strain data clearly shows damped, free response response in the 180 to 400 Hz range.

Regarding the NASTRAN modes, I concur with the questionable accuracy. I've got 36 NASTRAN modes below 400 Hz, and at least four discrete frequencies in the strain data. Somehow I need to convert the strain data into mode shapes, in order to estimate the peak stress.

Thanks
John

 

[GregLocock]

Yes, I thought from your first post you had a pretty good idea of what was going on.

Well, you seem to have a real problem, I can't see how to duck out of further work!

Absorbing high frequency vibration is possible - we do it with harmonic dampers. Trouble is, if ours fail, the car gets noisy. If yours fail, the structure breaks.

So I'd rather cure it in the metal itself, which comes back to extracting the modal amplitude from your strain gauge data or it might be worth extracting the strains from the Nastran deck, rather than trying to work with mode shapes as such. Then using your Nastran data and or a modal test to decide on a likely mode shape, and then strain gauge the high strain areas as a final check, or refine your Nastran model until you believe it and use that to predict the worst case strain.

Sorry, you did know the right answer, there is no short cut!


Cheers

Greg Locock

 

[hacksaw]

v~d,

It is generally difficult to excite the higher modes in a structure. Take a look at the modal participation. The dominant modes control.

 

[vorwald]

I've had to wrap up this problem, so I want to summarize what was done.

To recap, the problem is:
a) Strains were measured on a metal ramp under gun firing loading.
b) The corresponding stresses are below fatigue levels, implying long life.
c) However, several of the gauges have clear, damped, free response following the shot. The frequencies are in the 180 to 400 Hz range.
d) A detailed NASTRAN model has modes 16 to 40 in that frequency range

The problem is, what is the expected fatigue life. The concern is that there is modal amplification of the stress. In other words, there are locations where the stress is quite a bit larger than the gauge location.

The resolution consisted of:
a) Isolated the time segment after the first shot where the system is in free response
b) Applied sub-space algorithm on the frees response to estimate the state space matrices for the four gauges that had obvious free response.
c) From the estimated state space matrices, calculated the damping, frequencies, and (most important) the strain mode shape at those locations. Normalized the strain mode shape so the max gauge had a value of one.
d) Using the frequencies, and the location of the gauge with the max value, selected the NASTRAN mode that was closest to the frequency and with the NASTRAN strain distribution having the same maximum location as the estimated distribution.
e) This identified two modes that have symettric and asymettric deflection in a region of complex loading.
f) Using the NASTRAN strain/stress modal distribution, re-estimated the fatigue life in the regions of high stress / strain.
g) The system will be monitored in the suspect regions. If fatigue damage is occuring, corrective action will be take.

I've applied sub-space algorithm to five difficult problems in the last 14 months, 2 flight dynamics problems, and 3 structural dynamics problems. The sub-space algorithm is a time domain approach, applicable to multi input/output systems. The approach estimates the observability grammian, and from that information, proceeds to do a least square estimation of the A and C matrices, followed by the B and D matrices. A good reference is "REAL-TIME MODAL PARAMETER ESTIMATION USING SUBSPACE METHODS: THEORY",
F. Tasker, A. Bosse and S. Fisher, Mechanical Systems and Signal Processing. In that reference, the formulation for the A matrix is correct and possibly the C matrixs, but there is an error in the B and D matrices. Anyway, to use the method, you almost have to rederive the equations to understand them. The formulation presented only uses linear algebra, so rederiving the equations is reasonably straight forward.

If anyone is interested, I have rederived the equations, and implemented the formulation for free response in MatLab. Also, In Matlab, there is the N4SID method by Dr. Vanoverschee, which is also a subspace formulation, but the derivation of N4SID is not based on standard linear algebra. Also, the assumptions on sensor noise and system distrubances are different.

In the end, I believe the approach above allowed identification of the frequency and strain mode shape of the modes that are participating. Coupling this informaiton with NASTRAN gives a reasonable estimate of the fatigue life.

Cheers
J. Vorwald
vorwaldjg@nswccd.navy.mil

 

[vorwald]

A few people have asked why I didn't analyze this problem in the frequency domain. Initially, I did, but was unable to identify the natural frequencies confidently from the frequency response plots. However, from the coherence plots, I could identify likely frequencies. But there were inconsistencies in the coherence results. From the frequency domain results, it was only probable that structural modes were being excited. An alternative explanation was that the frequency results were a result of the frequency content of the loading.

I believe the difficulty in the frequency domain was a result of the loading. Here are the problems with the loading:

a) The loading was impulsive, so had a wide frequency content.
b) The time between impulsive loading was not constant, making the problem not periodic.
c) The loading itself was not repeatable, due to different initial conditions and other variations.
d) The loading was not measured, so it was difficult to extract out of the response.
e) The loading was applied to the structure at several distinct locations, and separately over a wide area.

In the end, the excellent agreement between the estimated time response (from state space matrices) and the measured time response conclusively shows the participation of the structural modes. The frequencies extracted from the estimated state space matrices were supported by the coherence plots. The frequencies could also be seen on the FFT plots, but the peaks did not dominate. The NASTRAN modes identified consisted of symmetric and anti-symmetric deflection under the area that was loaded. That region was not instrumented.