How to use frequency dependent soil siffnesses in Dynamic analysis ? 1

[dynamicd]

Currently I am designing concrete elevated frame type centrifuge machine (high speed as 60 cps) foundation and geotech report has given us frequency dependent soil stiffnesses. Geotech report shows that vertical stiffness gets in negative values after 30 cps for that perticular soil profile(there is a bedrock at 30 about 30 feet depth!).
Finite element analysis programs like SAP 2000 allows soil springs as one value irrespective of frequency. And SAP 2000 does not accept negative stiffness for vertical soil spring.

Please anyone has faced this type of problem of solving elevated concrete machine foundation with frequency dependent soil stiffnesses before or have you any thoughts what I should do!!!!!!!!!!

 

[Qshake]

I don't think that any of the products available are capable of doing what you're requesting. Therefore you must use your judgement as to how and what you want to model including what you output you expect and what you'd like to learn from this modelling.

Having said that, I would begin by ignoring the foundation springs and run an analysis which I would identify as the "fixed base" model. This model, depending on what your after may represent some upper limit of repsonse for the model.

Following that model I would then represent the structure with soil springs that are characteristic of the machinery operating at various frequencies that interest me. To understand what is of interest to me I would take a look at any dynamic text and review the principles of transmissibility. In reviewing this material I would think that the appropriate models would be obvious.

Once all the models are run, review and plot whatever response you have vs. Frequency and compare those to the upper or lower limit responses mentioned above. Design your foundation for the appropriate level.

You may want to check out Prakash's Soil Dynamics text as it includes a section on machine foundations.

Good Luck.

 

[ishvaaag]

Apart form modelling difficulties, the question is to guess a machine plus sbustructure assembly that never gets the subsoil excited in the dangerouns over 30Hz range.

You can start to assume ordinary compression only springs of the proper stiffness, expected for static solution.

Since you have starting frequency well over the range dangerous to the soil, then maybe trying to uncouple the machine from the foundation in various ways, spring plus damping may reveal one specific economical slab plus fittings that satisfies for the 60 Hz regime that all the main modes of vibration of the slab fall under the 30 Hz range.

One isolator usually avoids putting what at the other side at the same order of magnitude of vibration. One possible problem is that your specific machine wouldn't support isolators harder or softer than a given range -not complying being dangerous to the machine- or that them be a given, what would impair your ability to uncouple excitation from foundation vibration.

A complete model would comprise machine or "at least" its "equivalent" varying forces at support hardpoints, the supports modelled, the slab, and the soil. This model would give you what happens in the soil.

If you can't model the whole thing, maybe a model target for your case should be

Your (assumed) dynamic excitation is the (varying) load.

The loads varying this way are applied through the isolator/damping devices to the foundation, itself on the compression only ordinary springs.

Since we have more than anything the foundation in this model, its main modes of vibration will portrait IF the foundation is exciting the subsoil at dangerous frequency.

The transitory regimes shouldn't pose special problem but would be comvenient be checked as well.

A general alternative:

Some subsoil giving negative stiffness means to me at some time the soil is sucking your outfit downwards. Less than this I would have already thought my soil has liquefied. A liquefied soil? Since your problem is local, or even if it is building size, why not recurr to soil betterment? Investigate if soil stabilization technics are likely to succeed for your particular type of subsoil condition.

In any case it starts to be another way of adding mass to your foundation, be it from concrete, or from stabilized soil, to such extent it will become rarer and rarer the resonance develops.