Transient analysis for evaluating dynamic stresses 1

[elogesh]

Hai,

Usually I used to carryout the frequency response analysis for the design and analysis of new structures.I used to compare the response(displacement,velocity or accleration) less than existing or reference structures.This criteria primarily used for vibration specification.But I felt indirectly this assures the reliabilty(stresses) of the new system in comparison with existing or reference system.Whether Am I right? Ifn't please correct me.

Recently in one of project,I have asked to calculate the dynamic stresses.This landed me in transient analysis.The decision of chossing the time step was criticial process in this regard.I have choosen time period = 1/10*(inverse of highest frequency of interest).But the FEM data generated and solution time is considerably severe.Whether the procedure for calculating the time step is appropriate.
The dynamic load is almost impulse. total time for calculation choosen as nearly 3 to 5 time the duration of the application of the load.

The main question, whether it is possible to make decision about relaibilty and safety of a component subjected to dynamic loads based on frequency repsonse analysis.whether Transient response analysis is mandatory in this regard?

I will also post this question in FEM discussion forum.

If there is anything technically wrong,please correct me.

Regards,
Elogesh

 

[MikeyP]

Usually, the time-stepping integration in FE packages is carried out in the nodal (physical) domain. If your analysis is linear you can use the results of an eigenvalue analysis to carry out the time stepping in the MODAL domain. This means that the integrator is inverting a matrix of size n x n (where n is the number of modes in your frequency range) rather than N x N (where N is the number of degrees of freedom, ie the number of nodes x 6). I have obtained decreases in computation times of a factor of 1000 or more using this approach.

It is possible to do a non-linear analysis in this way, but it is not widely practised and we are still developing it for things other than beams and plates (!) watch this space...

M

M

 

[GregLocock]

Elogesh what you are doing sounds correct - make sure that your excitation signal is truly representative, and that your damping values are correct.

Cheers

Greg Locock

 

[elogesh]

Hai,

Mike,It is interesting to know that non-linear analysis can be attacked using modal formulation.We are definitely looking forward for it, for the real structures.

Greg, Unfortunately we don't have any reference of damping from experiments.We assumed constant damping as percentage of critical damping.

Regards,
elogesh

 

[GregLocock]

Hmm, that is a bit of a problem. If your damping is out by 50% for an important mode then your fatigue life could be out by a factor of 50 or so, not a very useful estimate. Perhaps you could run the same analysis on a known succesful structure.



Cheers

Greg Locock

 

[brad]

Mike and elogesh,
I'm not familiar with any "nonlinear mode-based dynamics" as suggested above. If this is indeed happening, I suspect it is more in the realm of simple hand calculations, not in more complex systems. I know of no commercial code that's even beginning to mention such ideas.

Brad

 

[elogesh]

Hai,

Brad, Probably I might have misunderstood the mike statement.


Regards,
Logesh.E

 

[GregLocock]

non-linear modal dynamics - I'm trying to wrap my head around that one. Is this related to the technique I use in ADAMS where a flexible linear structure is incorporated into a non linear system model by means of a modal reduction of the stiffness matrix of the flexible body?

http://www.mscsoftware.com/products/products_detail.cfm?PI=433

Cheers

Greg Locock

 

[MikeyP]

Brad, you are correct in thinking no commercial code can cope with a "non-linear modal model". However, the concept is relatively straightforward. Essetially we define a model of the form

[M]d2/dt^2([x]) + [C]d/dt([x]) + [K][x] + F{[x],d/dt([x])} = Q

The first 3 terms are the usual linear modal model. The function F is a series of non-linear terms which encapsulate the non-linear behaviour.

To perform such an analysis using FE, we first extract the linear modal model using ordinary eigenvalue analysis to get [M], [C] and [K]. We then do a STATIC non-linear analysis at several force levels for several different load cases (about 5 force levels for each linear mode of interest). We then do a regression analysis on this information to get the non-linear terms in F.

This whole process takes about 120 seconds of processor time for a 256 element model. The software has been implemented already using ABAQUS and NASTRAN and is being evaluated by the ministry of defense in the UK. I am running a 2 year project to develop an experimental version of this process which is essentially a non-linear experimental modal analysis. This works a little differently. Instead of the static load cases in the FE analysis we use a series of sinusoidal bursts applied to the structure to gather the data required for the regression analysis.

The whole point of this approach is that it DOES allow us to work with systems that are complicated structurally. Other than our work, it is rare to see anything other than 2 or 3 degree of freedom systems analysed non-linearly. But we have already sucessfully identified an FE model of rib/stringer stiffened plate (first 5 modes) with results essentially identical to those of ABAQUS time stepping but taking 5 minutes rather than 5 days to complete! On the experimental side I have identified a non-linear model of a clamped plate in the lab (well the first 3 modes at least) and in simulated experiments we have identified a 9 degree of freedom system.

Like I say, watch this space...

M

 

[zzy]

long time ago, I used a linearization approach for transient problems with modal data (frequency, mode shape, damping). The concept is very simple. If you have a total time of T over which some nonlinear behavoirs are expected. You first divide T into a set of sub-intervals, T1, T2, ....Tn (T1+T2+...+Tn=T). Depending on your problems, each sub-interval needs to be small enough so that modal parameters (frequency, mode shape) do not vary lots. For each sub-interval, you carry out modal analysis to extract modal mode and then use them to get time response in a similar way as modal superpositions. You do that from one sub-interval to another until reaching the end of T.
I applied this to transient response of mechanisms (linkage) with multiple slender parts and very high speed (i.e., high inertia excitation). In comparison with direct-integration method, it was faster and there was no much difference in result.
If you are interested, I can refer you to some published papers on ASME Tranction Journal or International J. of Mechanisms and Machine Theory.

 

[pja]

MikeyP,
We are doing some similar work with regards to a fluid-structure interaction problem. We plan on publishing
the work soon. It's a very good idea if you know apriori the
form of the nonlinearity..ie this works well for a geometric
type nonlinearity.

 

[MikeyP]

Exactly pja. The current research is a joint programme with another university. We are looking at the practical experimental side. They are looking at ways of identifying the underlying nature of the non-linearity (geometric stiffening/friction/bilinear stiffness/backlash etc) to determine the basis functions which should be used in the regression. Of course many of these types of non-linearity may be approximately represented by higher order polynomials and an approximate model is what we are trying to achieve.

M