## fatigue analysis:frequency domain vs time domain

I have read a lot of paper about fatigue damage, in some fields it is particularly used the time domain approach while in others the frequency domain approach, but I haven't understood when it is better to use frequency approach respect time domain approach. May you help me to understand better this?
Thanks
 The decision whether to go for a frequency domain analysis or a time domain analysis is not straightforward, and there are some main factors you should account for. I will try to summarise, but beware they will not be enough to assure anyone that the "best" approach will be attained. Often, frequency domain analysis cannot be replaced by a time-domain analysis, when you know, or expect, or are required to verify whether the structure will respond dynamically with the excitation load frequency (like aerolastic structures, wings, blades, tall buildings, towers, bridges, pipelines, risers and structures subjected to VIV or resonance with local machinery like vehicles, ships, steel frames, machinery foundation, acoustic loads...). If one decides to work in the time domain with these types of structures, one might overlook any dynamic amplification factors and will get a wrong expected life (wrong cumulative damage, wrong stress cycles) and maximum expected stress might be significantly off (low RMS stress, low peak stress, wrong stress ranges). In the frequency domain, you must feel confortable working with load spectrum, mode shapes, response analysis, harmonic analysis/transfer functions, linearizations, statistics, damage computation methodology, damping factors and simplified equivalent models to keep the analysis reliability under control. In the time domain, usually one will be working with large load data, that will require significant computational power and labor, but one might feel more in control of the analysis process and routines. Complex problems can be verified directly in the time domain, whether the frequency domain analysis usually requires simplified models (beam models, equivalent models, analytical models) to get the results within schedule, specially with changing designs. Sometimes, a time-frequency hybrid analysis is more indicated to let one benefit from both the time domain capability of working faster with complex shapes\structures, and from the frequency domain capability of verifying global and local dynamic responses under random or harmonic excitation loads, in these cases FFTs are applied to translate from one domain to the other and back again, retaining reliability.
 Recognitions: Science Advisor It depends on the type of loading and the fatigue life you are interested in. In some situations the excitation force is a single-frequency harmonic force almost by definition (for example a machine with a rotating component that is not perfectly balanced) and the structural response is linear (because you would want the fatigue life to be of the order of millions of cycles, therefore the loads would be relatively small relative to the strength of the structure.) On the other hand some fatigue situations have a nonlinear response and a relatively low life requirement - for example setting the limit on the number of heavy landings that are allowed for an aircraft before a mandatory inspection procedure is requred. (The fatigue limit could be as low as one cycle!) The frequency domain would be the obvious choice for the first case, and the time domain for the second.

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## fatigue analysis:frequency domain vs time domain

 Quote by john.phillip Often, frequency domain analysis cannot be replaced by a time-domain analysis, when you know, or expect, or are required to verify whether the structure will respond dynamically with the excitation load frequency (like aerolastic structures, wings, blades, tall buildings, towers, bridges, pipelines, risers and structures subjected to VIV or resonance with local machinery like vehicles, ships, steel frames, machinery foundation, acoustic loads...). If one decides to work in the time domain with these types of structures, one might overlook any dynamic amplification factors and will get a wrong expected life (wrong cumulative damage, wrong stress cycles) and maximum expected stress might be significantly off (low RMS stress, low peak stress, wrong stress ranges).
Why do you think time domain analyses cannot be performed often? Most always one should analyze a dynamic system in the time domain to get the most accurate results...especially with risers. The reason being is that the lateral effects are not accurately assessed with a frequency domain method due to highly non-linear terms in the equation of motion. A frequency domain method requires the non-linear term to be linearized which is not as accurate.

No dynamic factors will be over looked when using a time domain approach. The full equation would be solved at each node for each differential time step yielding a full solution. Of the two methods, a frequency domain solution will have more error. The only deterrent to using a TDM is that it requires more computational power and thus more time. However, with modern computers it is not an issue.

CS

 Quote by stewartcs Why do you think time domain analyses cannot be performed often?
I did not state that, what I am saying is: "Often, frequency domain analysis cannot be replaced by a time-domain analysis".

 Quote by stewartcs (...) The reason being is that the lateral effects are not accurately assessed with a frequency domain method due to highly non-linear terms in the equation of motion. A frequency domain method requires the non-linear term to be linearized which is not as accurate.
You are very right here, except that you are implying that by linearizing you are inevitably\permanently losing the analysis accuracy, which is not always true. Depending on the type of analysis you are interested in, you can keep the analysis reliability working stochastically, calibrating with lab tests and/or proven simplified\parametric models. Riser fatigue analysis will be inaccurate in the frequency domain due to the inability to predict the extreme responses (providing a Gaussian response instead) and for the reason you mentioned, but there are mathematical models and available data for other types of structures that accurately or conservatively predicts their extreme responses when working in the frequency domain. Another aspect is the rainflow cycle counting, typical of time domain fatigue analysis, that can ruin the analysis accuracy if not sampled correctly. In the frequency domain, cycle counting can be assessed accurately by working with zero-cross frequencies (Just to state the fact that analysis accuracy is not only a matter of the chosen domain).

 Quote by stewartcs The only deterrent to using a TDM is that it requires more computational power and thus more time. However, with modern computers it is not an issue.
By mentioning risers, you gave an excellent example where a full time domain analysis is the best approach, and actually the only one acceptable for risers by classification societies nowadays, mainly due to the benefit of faster computers as you mentioned, but you should bear in mind that risers are springlike (can be represented by unidimensional elements), so although their analysis due have its complexities, one cannot compare risers with other engineering structures that can only be appropriately represented with bidimensional and three-dimensional elements, pushing the degrees-of-freedom significantly and driving computational time beyond the economical boundary, demanding computer clusters, full scale lab simulations, mathematical models and/or conservative simplified analysis. Compared side-by-side, this higher computational solution time is usually felt more in the frequency domain.

 Quote by stewartcs No dynamic factors will be over looked when using a time domain approach.
I got pretty curious about how are you getting VIV responses from a full time domain analysis, but by rereading you, I got the feeling that you are talking about dynamic loads (hydrodynamic) while I am talking about structure response through dynamic amplification factors (DAF): "(...) one might overlook any dynamic amplification factors and (...)"

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 Quote by john.phillip By mentioning risers, you gave an excellent example where a full time domain analysis is the best approach, and actually the only one acceptable for risers by classification societies nowadays, mainly due to the benefit of faster computers as you mentioned, but you should bear in mind that risers are springlike (can be represented by unidimensional elements), so although their analysis due have its complexities, one cannot compare risers with other engineering structures that can only be appropriately represented with bidimensional and three-dimensional elements, pushing the degrees-of-freedom significantly and driving computational time beyond the economical boundary, demanding computer clusters, full scale lab simulations, mathematical models and/or conservative simplified analysis. Compared side-by-side, this higher computational solution time is usually felt more in the frequency domain.
I don't know of any classification societies that require a specific method...although they may recommend one or the other.

Risers are actually one of the more complicated structures to model in engineering. I'm not sure why you think they don't compare to others...perhaps you could provide an example. Risers are typically modeled as either a tensioned beam (with appropriate modifications) or a mass-spring-dashpot system. They have complex responses that are very sensitive dynamically. They have complex loadings from vessel interactions and direct hydrodynamic loading.

Risers can be modeled in either 2D or 3D so the computational time will vary depending on which is chosen - with the 3D model being the longest. Of course the number of nodes, mesh, and simulation time will greatly affect it as well. The 2D model is generally more conservative since the environment is collinearly applied.

 Quote by john.phillip I got pretty curious about how are you getting VIV responses from a full time domain analysis, but by rereading you, I got the feeling that you are talking about dynamic loads (hydrodynamic) while I am talking about structure response through dynamic amplification factors (DAF): "(...) one might overlook any dynamic amplification factors and (...)"
I'm not sure what you mean. There is no need for DAF since the riser is being analyzed dynamically. In other words, one only needs a DAF to account for the dynamic response if one is modeling a structure statically or quasi-statically. Since the equation of motion of a riser includes dynamic effects, they are inherently captured in the solution.

Riser fatigue is normally attributed to VIV and WIV (wave induced vibrations). The total cumulated fatigue damage is the sum of the two. Normally a program such as Shear7 or VIVA are used to find the modal response of the riser (which is done in the frequency domain IIRC) insofar as VIV is concerned. However, VIV analysis can certainly be done in the time domain as well, again, to accurately capture the non-linearities. WIV is typically done in the time domain too for the same reasons. The non-linear response of the riser cannot be overlooked.

CS
 So in conclusion in presence of shocks, or nonlinearities in general, frequency analysis isn't good enough, is it? Moreover I think in some solution in the time domain analysis it is good enough to compare the fatigue damage caused by two different conditions in which I think it is very important to understand the damage behaviour with frequency. Take for example the comparision between military vehicle life and the corrisponding proving ground test. That vehicle aren't used to run on road so it is necessary to compare the excitation frequency for making sure all vehicle sub-systems are excited in the right way. In your opinion, am I in fault?

 Quote by stewartcs I don't know of any classification societies that require a specific method...although they may recommend one or the other.
I will try to clarify based on DNV standard OS-F201 Dynamic Risers (http://exchange.dnv.com/publishing/C...10/os-f201.pdf). In fact, there are no explicit requirements to design based solely on a time domain analysis, but there are three interesting tables on page 25. Tables 4-1 and 4-2 provide an overview of NTD, LTD and FD techniques and their applications. Table 4-3 establish analysis validations based on the chosen technique. What stands out for me is that the NTD analysis is preferred and the other methods are treated as simplified (table 4-2), requiring further validation through NTD. So, it looks like to me that, in the end, NTD analysis is a requirement.

 Quote by stewartcs Risers are actually one of the more complicated structures to model in engineering. I'm not sure why you think they don't compare to others...perhaps you could provide an example. Risers are typically modeled as either a tensioned beam (with appropriate modifications) or a mass-spring-dashpot system. They have complex responses that are very sensitive dynamically. They have complex loadings from vessel interactions and direct hydrodynamic loading.
It is wrong wording from myself, as I am relating the word "complexity" with computational time (hard to compute) rather than Engineering modelling complexity (hard to design). I am pretty sure risers are hard to model properly and to validate.

 Quote by stewartcs Risers can be modeled in either 2D or 3D so the computational time will vary depending on which is chosen - with the 3D model being the longest. Of course the number of nodes, mesh, and simulation time will greatly affect it as well. The 2D model is generally more conservative since the environment is collinearly applied.
Are 2D and 3D meshes generally applied for local model screening only? If so, this puts riser analysis more on the 1D side, meaning faster to solve.

 Quote by stewartcs I'm not sure what you mean. There is no need for DAF since the riser is being analyzed dynamically. In other words, one only needs a DAF to account for the dynamic response if one is modeling a structure statically or quasi-statically. Since the equation of motion of a riser includes dynamic effects, they are inherently captured in the solution. Riser fatigue is normally attributed to VIV and WIV (wave induced vibrations). The total cumulated fatigue damage is the sum of the two. Normally a program such as Shear7 or VIVA are used to find the modal response of the riser (which is done in the frequency domain IIRC) insofar as VIV is concerned. However, VIV analysis can certainly be done in the time domain as well, again, to accurately capture the non-linearities. WIV is typically done in the time domain too for the same reasons. The non-linear response of the riser cannot be overlooked." CS

I asked about VIV and DAF because VIV is usually either assessed in the frequency domain, or through a hopefully conservative numerical\empirical simplified model, so a time domain analysis will not inherently capture these effects unless the environmental loadings somehow include them (loads from lab tests, perhaps from a validated CFD analysis or from empirical numerical methods). Hence, a time domain analysis will not accurately predict the fatigue life without accomplishing other analysis, including frequency domain analysis to capture the modal\response spectrum, numerical modelling or by relating to VIV load data.

 Quote by john.phillip The decision whether to go for a frequency domain analysis or a time domain analysis is not straightforward, and there are some main factors you should account for. I will try to summarise, but beware they will not be enough to assure anyone that the "best" approach will be attained. Often, frequency domain analysis cannot be replaced by a time-domain analysis, when you know, or expect, or are required to verify whether the structure will respond dynamically with the excitation load frequency (like aerolastic structures, wings, blades, tall buildings, towers, bridges, pipelines, risers and structures subjected to VIV or resonance with local machinery like vehicles, ships, steel frames, machinery foundation, acoustic loads...). If one decides to work in the time domain with these types of structures, one might overlook any dynamic amplification factors and will get a wrong expected life (wrong cumulative damage, wrong stress cycles) and maximum expected stress might be significantly off (low RMS stress, low peak stress, wrong stress ranges). In the frequency domain, you must feel confortable working with load spectrum, mode shapes, response analysis, harmonic analysis/transfer functions, linearizations, statistics, damage computation methodology, damping factors and simplified equivalent models to keep the analysis reliability under control. In the time domain, usually one will be working with large load data, that will require significant computational power and labor, but one might feel more in control of the analysis process and routines. Complex problems can be verified directly in the time domain, whether the frequency domain analysis usually requires simplified models (beam models, equivalent models, analytical models) to get the results within schedule, specially with changing designs. Sometimes, a time-frequency hybrid analysis is more indicated to let one benefit from both the time domain capability of working faster with complex shapes\structures, and from the frequency domain capability of verifying global and local dynamic responses under random or harmonic excitation loads, in these cases FFTs are applied to translate from one domain to the other and back again, retaining reliability.
Do you have some references (books or papers) to suggest me?
Thanks
 I might have, what are you looking for?

 Quote by john.phillip I might have, what are you looking for?
I know nothing on hybrid time-frequency domain analysis, so I'm looking for some theory the understanding the method and In particular, I'm interested in automotive applications.
Thanks

 Quote by john.phillip I might have, what are you looking for?
Hi John, have you found some interesting material?

Thanks