Why is the natural frequency of structures required for seimic? 1

[VoyageofDiscovery]

As I understand it, the natural frequency of a structure determines when a structure can resonate to collapse given enough time.

For seimic design, outside of resonance, why do computer programs for seismic analysis go through the process of finding eigenvalues when determining seismic forces?

VOD

 

[Qshake]

VOD,

Resonance is only part of the problem. Though it is a very important part it is also very difficult to pinpoint matching.

Simply put the real, or let's call it widespread, problem is how the structure can or will resist the tendency to move laterally. Just as if you were in a car moving along with some velocity and was abruptly stopped, everything not bolted down in the car will tend to continue moving with the same velocity. Presumably you'll be wearing a seatbelt and that seat belt must act in such a way (if its to be successful) as to restrain the person. The seat belt can do this in a number of ways...the belt will remain elastic such that you won't move at all or very little and the belt itself is not damaged. Secondly the belt could yield a small amount which would allow the driver to move a bit and possibly engage the airbag. That might be thought of as controlled damage. Or the belt could simply fail which may be thought of as a catastrophic failure. Seismic design philosophy for structures follows along the same lines.

So it boils down to inertial forces/restraints. Thus the more mass that is excited the worse the problem can be. It is also possible that the amount of mass is so large and the ground motion sufficiently small as to preclude excitation. For many years it has been thought that by adding weight to buildings at the top, for example, will mitigate some of the problems. Adding water tanks to the top of buildings adds mass but also adds some damping factor as well.

We could go on and on about the relationship of stiffness, mass, period and damping all of which work together to define the vibration problem. Hopefully some of the aforementioned was helpful.

Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[Lucifer67]

The reason is relatively simple....

In structural dynamics there is an "orthogonality property of the modes of oscillation".

You may ask what is this...

It means essentially that you can decouple the equations of motion, solve for each mode independently and combine the effects of each mode to obtain design forces.

The starting point then is to identify the frequencies of the system. In this respect mass participation is essential and normally you would process enough modes to obtain 90% MP. It does however depend on the type of structure; in some instances the dominant mass is at or above the ZPA (perceived to be around 33Hz). In this instance you would use a missing mass calculation to ensure you have the correct force in the system.

So assuming you have the correct number of modes to capture the mass you would calculate the force in each mode subjected to the design earthquake in direction x (say).

You would then combine the results of the modes into a single set of forces. This is generally referred to as a modal combination, methods used can be SRSS, CQC + many others.

The final step would be to combine the effects of the earthquake in the 3 principal axes (if/where necessasry). This is generally referred to as a spatial combination.

So the steps are as follows

1. Frequency extraction
2. Modal combinations under design Spectra
3. Spatial combinations of earthquake directions

 

[dawn836]

well that are n ice answers from both QSHAKE & Lucifer67
i have a question may be it is easy but it confuses me much

Does the mode of vibration have a physical meaning?

 

[VoyageofDiscovery]

Thanks for the replies,

What I am really driving at is, there is natural frequency and there are excited frequencies. How does finding natural frequency play into the analysis using excited frequency.

VOD

 

[Lucifer67]

All,

In terms of physical meaning, the dominant mode is the one that dominates the response of the system.

If one were to "ping" (technical term) a tuning fork the same would respond in modes 1,2,3,4 etc. However the vast majority of the response will be governed by mode 1. The higher modes contain very little mass and would not contribute greatly to the response. You should bear in mind that when a structure is "pinged" it vibrates in all modes at the same time; some being more dominant than others.

There are numerous suggestions that state a dominat mode is one that has more than x% mass. However this quickly breaks down when considering complex 3d structural problems.

Additionally it also becomes a function of the frequency content of the input motion.

If you had a simple system with 3 modes you might have mass participations in each mode of 80, 10 and 10%. Clearly mode 1 would be considered as the natural frequecy.

Alternatively you may have 10, 10, 80 where mode 3 would be considered as the natural frequency.

But if you have 33, 33, 33% you have 3 modes that need considering.

In real terms the Engineer needs to be cogniscant of the frequency content of the input motion. In that one needs to examine the modal frequency, mass participation and force.

The combination of all 3 may make a lower mass mode dominant in terms of forces developed in a system.

As discussed the concept of natural frequencies and fundamental modes rapidly breaksdown when considering complex 3d distributed mass and stiffeness sytems with say 1000 modes.

Hope this helps!

 

[dawn836]

as of my small knowledge about modes of vibration and participation mass that when i analysis a frame of 3 modes of vibration (3 story frame)
i get he following results:-

1-First mode with lower frequency have highest participation factor and the three storys have drift in one direction

2-Second mode with higher frequency than first mode
and have less participation factor and two storys move in one direction while the third move in other direction

3-third mode higher frequency than second modeand have less participation factor and two storys move in one direction while the third move in other direction (drift will be other combination than what happend in mode 2)

as a conculsion i can get that the participation factor is always the highest for the lowest mode of vibration in frequency

The real drift of the storys is the one i can get when i combine the three modes toghter.

what i said above is correct or there is some points i miss?

 

[Lucifer67]

Your conclusion is incorrect in that the lowest mode automatically contains the highest mass.

It just so happens that the 3DOF system you are considering happens to have the predominance of the mass located in mode 1. This should not be considered as a generalised case for all modal analysis.

If you had a water tank on top of your frame you would need to create an analogue for the fluid behaviour. In this respect it is highly likely that the modes of the fluid would be the lowest.

Likewise this mode (say mode 1) would contain the majority of the impulsive fluid mass and none of the structural (frame mass). Since the frame contains more mass than the fluid the highest mass mode would probably be mode 2 (shear mode).

By far the best example is the analysis of suspension bridges or cable stayed structures. If you were to model a suspension bridge you would model the deck and hangers. Each hanger would have its own modes of oscillation. Each hanger would be of a different length and therefore you will have guzzillions of low energy, low frequecy modes. All these modes have negligible mass as it is all located in the deck system.

However somewhere above all these spurious cable modes is the deck mode with a stonking amount of mass, and that is the one you would want.

For this reason most international codes require that the frequency extraction encompass 80-90% of the total structural mass.

I hope this helps, or am I merely adding to your problems.

Lucifer

 

[VoyageofDiscovery]

dawn836,

Please answer my question or show me the courtesy of starting your own thread if you have a question. As far as I can see your question does not relate.

VOD

 

[4Pipes]

Yet again, the replies are amazingly genourous. People are willing to give the benefit of years of difficult study to people do not appear to have a basic understanding.

I am not against sharing knowledge with similarly qualified peers but I would draw the line with people who do not understand the fundamental principles of the subject. I would assist them but only if I knew they were spending as much study time and money as I did.

I used to do "free teaching" regularly until I was finding people standing up in meeting, declaring themselves experts and using my buzzwords. In many places, including the UK, the equivalent of degree + PE status is not required in many disciplines. One of the few exceptions in the UK is Structual but then again you don't necessarily need to understand dynamics of structures.

All that is required to get involved with at least some parts of the design some of the most complex of systems including nuclear is a vocabulary. (You may scoff). I have lost out in contract jobs on more than one occasion to people whose only knowledge was a few appropriate words and the ability to input data into suitable software - and of course tell the boss that the job is complete - the most important qualification of all after being able to talk your way into the job in the first place.

EngTips is a brilliant concept but should not be used as a quick way to obtain basic knowledge. It will put others off contributing.

The reply to this quite reasonable question should have been to recommend a training course or a text book. Several good text books have been mentioned in earlier posts. I am in no way criticising the original post.

 

[pdiva]

VOD,

Simply saying, the natural frequency tells you how the structure is flexible; Long period structure is more flexible than short peroid structure.

 

[UcfSE]

The natural frequency appears in the solution of the differential equations describing free vibration. It also appears in the solution methods of other types of vibration including harmonic and unit-impulse. The natural frequency may also be used to evaluate the validity or stability of numerical solution methods. Similar to how you need stiffness to evaluate structural response to static loads, you need the natural frequency to evaluate response to dynamic loads.