Time History Analysis with Shock Absorber

[Anonymous]

Dear

I am modelling the following structure : the equipment (sensitive equiment) supported by 4 shock absorber subjected to base excitation. Anyone knows how to model this kind of structure as a SDOF system ? I could not find the straightforward way in RSAP, so i dicided to model it as a canteliver (using equivalent spring analogous lateral stiffess 3EI/L3 at top) and add mass at top (using load to mass conversion, active mass direction in x-direction for base excitation in x-direction , using Newmark (acceleration) to input the accelogram (Direction X)) but the results not very logical. The displacement is almost the same no matter how i reduce the stiffness of the canteliver (by reducing the section) ot increase the mass at the top (did things which is supposed to increase the displacement). I attach the file as well as the accelogram. 

Thank you for your support.

[Pawel.Pulak · Accepted solution]

Hello,

it can be modelled also in the way you did. 

As concerns your remarks that "The displacement is almost the same no matter how i reduce the stiffness of the canteliver (by reducing the section) ot increase the mass at the top (did things which is supposed to increase the displacement)" I have not observed such effect:

1. the model is defined without any dumping and the excitation results it steady state oscillations of the frequency of 3.8 Hz (coherent with modal analysis) and the amplitude of about 17mm
2. after changing the section to for instance UC 305x305x97 the frequency changed to 4.67 Hz and the amplitude to about 10 mm
3. not changing the section but doubling mass resulted in decreasing the frequency to 2.71 Hz (as expected division by sqrt(2)=1.41 factor) with he amplitude still equal to 17mm

Generally for the excitement of this type you will not observe pure resonance behaviour.

As concerns different ways of modeling this structure it can be done using for instance compatible nodes - as in Tuned Mass Damper (TMD) creation with RSA post.

I have attached the example illustrating it (without time history analysis). Robot "does not like" models with only nodes and without any elements so it was necessary to add some dummy bar.

The advantage of this way of modeling is that if you will need to define some viscous dampers it can be easily done inside the definition of compatible node (it can be done also in releases or in supports)

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Regards,

[Anonymous]

Thank you very much, i understand the problem now.

[schen74UN5]

Hello Paul, 

I see thoses interesting discussions by researching the THA in the forum, and I found your discussions inspirng. 

I'm doing a study by using RSA, i know that we can give  viscous dammping values in the model in release. 

My question is how do we define the damping values, do we calculate it? or this is something we can find in the books? 

Thanks 

[Pawel.Pulak]

Hi,

damping constant (expressed in force/velocity units) is a property of the specific model of viscous dampers - to be found in the fabricators' catalogues.

Remember that Robot supports only linear viscous dampers.

Regards,

[schen74UN5]

Thanks for your quick response Pawel, 

somehow, I have some doubts on how should we define parametres in modal analysis for preparing the time history analysis. 

The situation is that I want to study a structure with Shock absorbers which isolate upper strcuture from lower structure. so i defineD a damping coeffient (=0.3) by using release function which is only acceptable in timehistory analysis. 

But when i launch the modal analysis, the daming value is always 0.05, that suprise me beacuse i defined a value much higher than 0.05 in release. 

How should i do?  does the parametres in THA change the modal analysis results? 

Thanks a lot

[Pawel.Pulak]

Hi,

short explanation to damping values which can be defined in various places in Robot:

1) Damping defined in advanced parameters of modal analysis - it is a relative damping used ONLY in seismic analysis (following the specific modal load case) to modify response spectra to consider specific damping

a) It is also possible to activate there "Include damping in calculations (according to PS92)" check-box. In such case the final relative damping is calculated for each mode from relative dampings of materials composing different parts of the model and relative dampings of releases, supports and compatible nodes contained in the model, where "Damping according to PS92" was defined. These different components of damping are combined for a specific vibration mode in a way proportional to elastic energy of deformation corresponding to these parts of the model (the formula from part 6.2.3.5 point 3) of the code NF P 06-13).

2) Damping defined  in releases, supports and compatible nodes

a) Damping defined directly on the Damping tab and expressed in force/velocity or moment/ radial velocity units defines linear viscous dampers used in linear time history analysis using Newmark, Newmark (acceleration) or HHT method.

b) Damping defined when using  "Damping according to PS92" button from the damping tab, is a relative damping  used in seismic analysis in case 1)a)

3) Various types of damping available in time history analysis:

a) Modal relative damping available in modal decomposition method of THA

b) Rayleigh damping - damping matrix created as some linear combination of stiffness matrix (Beta coefficient) and mass matrix (Alpha coefficient) - available in Newmark, Newmark (acceleration) and HHT method.

c) numerical damping - available in HHT method (Alpha coefficient less than 0)

d) and indirectly viscous dampers defined in point 2)a) above and used in Newmark, Newmark (acceleration) or HHT method for linear time history analysis

4) Modal relative damping or Rayleigh damping available in harmonic, FRF and footfall analysis

I hope it explains your doubts. The value of damping shown in modal analysis does not influence time history analysis - as stated above it can be used only is seismic analysis.

Regards,

[schen74UN5]

Thanks, this resumé is very helpful. 

This clarifies certains doubts I had. 

I'd like to have your enlightments related to the Reyleigh method for determining the dampings in the Newmark (acceleration) option. How should we define the pulsation values w1 and w2 for calculations of alpha and Beta?

And can we activate both damping defined in THA and that defined in the releases at the same time, or only one of these should be taken into consideration?

Thank you. 

[Pawel.Pulak]

When selecting the values of pulsation to calculate Alpha and Beta the article available here may be useful.

It is possible to use simultaneously the "distributed" Rayleigh damping and the damping of viscous dampers defined in releases, supports or compatible nodes.

Regards,

[schen74UN5]

Thanks Pawel,
I'll look into this.

Another question I have during my study: For a relative complex spatial structure, there will be principal mode for each direction (X.Y.Z) of vibration, how should we design the TMD that helps to damp the vibration from all directions? When we calculate the added mass to the compatible node simulating a TMD, Which modal mass should we take? Do we take always the first mode modal masse in order to determe the mass of TMD? which seems more raisonable to me, because the TMD will be the same for all directions.
Could you give your opinion upon this question?

With repect to the mass of TMD, I saw in one of your posts that is equal to 5% of modal mass of fisrt mode, is that a rule to be implemented in all cases?

Thank you.


I hope I formulate the question properly.

Thanks

[Pawel.Pulak]

It will be difficult/impossible to find TMD which will be efficient for many modes.

Tuned mass damper is as the name suggests tuned to specific mode.

In my forum post available here I have done it for the first mode - but in general case it can be for any mode.

Regards,