structure dynamics 1

[flyby911]

hello fellow engineers
i've been reading in the building dynamics field and i think i'm missing something

1-i understand the physical definition of the natural frequency but (is it the reciprocal of the periods at which the different mode shapes take place)?

2-due to seismic action does the structure vibrates by the same frequency of the ground vibration frequency or structures respond by different frequency of the ground frequency

3-if (NO.1) is right , how come we enter the response spectrum curve with the modal periods to get the ground acceleration value and then the lateral force? (that's a hazardous case as i understand)

 

[UcfSE]

1. frequency is the reciprocal or period.

2. the structural response is dependent on several things and is not equal to the ground motion.

3. the spectral acceleration or pseudo-spectral acceleration is structural response, not ground motion.

 

[flyby911]

UCFSE thanx for the reply

i meant are the periods of the mode shapes are the natural periods or they are just periods that these modes will occur?

2-the response spectrum curve that's provided by the different loading codes is for the ground or for the structures?

 

[hippo11]

All structures have many, many periods with corresponding mode shapes. These periods and corresponding mode shapes are inherent to the structure and are independent of your input frequency (earthquake, wind gusts, vibrating machinery, etc.)...

The "fundamental" period of your structure is the one that has the lowest frequency/highest period. It's basically the mode shape and frequency that would dominate how the structure would "want" to vibrate if you took a giant thumb and "plucked" your structure, depending on which direction you would "pluck" in...

If instead of "plucking", you input a vibrating force with a given frequency (earhquake, wind, vibrating frequency), your structure would react with a mode shape/frequency that's dominated by the characteristic mode shape/frequency that has the closest Hz to the input Hz. Basically it would react with a combination of its inherent mode shapes/frequencies, but it would be "excited" by the one inherent period closest to your input period....and of

At least that's how I understand it....

 

[271828]

Structures have lots of natural modes of vibration. Each of these natural modes has a frequency (1/period) and a shape.

If you apply a sinusoidal load (or base excitation) with frequency "f," the structure will vibrate at frequency "f" regardless of its natural frequency. If this force frequency equals a natural frequency, then the response will usually be much larger.

 

[UcfSE]

You should check out or buy a text for this. Chopra's text is probably the most widely used and is an excellent text for structural dynamics. I suggest that to you because your first question in your second post doesn't really make sense. You should read up on the basics, and a good text like Chopra's will help you with that.

The second question was asked and answered. Think about the term "response" and what it means, i.e. response of what?

 

[271828]

UcfSE, I don't understand: "2. the structural response is dependent on several things and is not equal to the ground motion."

The response isn't equal in magnitude to the ground motion, but the frequencies are related.

If the ground motion (input) was somehow a single sinusoid at a frequency f, then the response would be at frequency f. The confusing thing is that the input is composed of a wide range of frequency content. In other words, a bunch of superimposed sinusoids of different amplitudes, frequencies, and phases. The structure's response to each individual sinusoid is still at that individual sinusoid's frequency. Superimpose the responses to all these input sinusoids to get the response to the total ground motion.

I second the Chopra recommendation, BTW. It's the only such text I know of that's readable, in a reasonable timeframe and amount of effort, to most structural engineers.

 

[zaes73]

1) in an event of ground motion the time taken for a fixed number of occurrences(mode shapes) is frequency of the building, rather than the number of occurrences within a fixed time. The other way around meaning the number of occurances within a fixed time is time period. therefore Frequence is the opposite(reciprocal) of time period.

2) every structure on ground has a different frequency, in the earthquake with a specific frequency different structure respond to it with different frequencies. for example a three story building will have different frequency and a twelve story building will have different frequency.

3) response spectra is simply a plot of maximum response (max displacement, velocity, acceleration ) usually the response spectras you derive from the A.S.C.E. or U.B.C. to induce to you building to get buildings different frequencies and mode shapes, is simple ground accelaration against time period of ground, in a certain time (6, 8 etc. seconds)

i hope this helps.

 

[UcfSE]

Superimpose the responses to get the total response, which will not be the same as the ground motion. A structure at a given natural period will not respond to a given earthquake the same as a structure with different properties. Initially, the transient response (dependent on the structure properties) governs over the steady state (dependent on the forcing function). Because the response then depends on the structural properties, the structure will not respond with the same frequency as the ground. If the earthquake lasted a long time at the same frequency, the structure would eventually reach the steady-state response and vibrate at the same frequency as the ground. Earthquakes don't do this.

Quantitatively, you can pick a ground acceleration recording and solve the equation of motion for a range of periods for a given damping ratio and see what happens to the frequency of the structural response.

Imagine that a very stiff building will repond very similar to the ground motion while a very flexible one will respond much different.

 

[flyby911]

thanx for the replies , and thanx for the chopra's text recommendation it's been a useful text to get the missing things..

now that i got that the response spectrum is a plot of the maximum response of STRUCTURES with different natural periods.

in design of structures...how to prevent excitation??..how to control that the earthquake's frequency will not make resonance with one of the natural frequencies of the building??..can it be avoided?? or it's a matter of luck?

 

[zaes73]

Its a matter of experience, i used to hear my senior engineers that in a good building design the one with Iy of the structure close to Ix of the structure, and some other stuff like that, I slowly realized these are actually tips and tricks to reduce the frequency of the building and improve buliding dynamic response behavoir!

offcoarse there is no structure with zero frequency. but more stiffness and intelligent layouts can reduce it . Tubular design of buildings is a therefore adapted for high rise buildings.

 

[271828]

"offcoarse there is no structure with zero frequency.... "
Sure there are. Not bldg structures we'd want to design, though!

 

[zaes73]

"Sure there are" for example ?

 

[apsix]

A rock fill dam?

 

[GregLocock]

cars ships aircraft

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[zaes73]

cars, ships, aircrafts, and specially rockfill dams all have frequencies, all vibrate in under Dynamic loadings, the designers do perform dynamic analysis on all of these structures.
for Rock fill dam : water pounding impact

for Aircraft : specially wings are designed for dynamic jet wash, or lateral wind gusts etc. (

http://ntrs.nasa.gov/search.jsp?R=481101&id=5&qs=No=40&Ne=26&N=270

)

for Ships : fluid pressures cause the ship to vibrate.(

http://www.marin.ntnu.no/~callas/DR_ING_Vikestad.pdf)

 

[dgkhan]

Looks like the saying that" dynamic analyis will give lesser
design values than static analysis" does not hold any more, as we educate ourselves more and more with dynamic loads. We should do static analysis for gravity loads and dynamic analysis for lateral loads (wind and Seismic).

 

[GregLocock]

sorry zaes73, cars ships and aircraft all have zero frequency modes. They are called rigid body modes, and are due to the unconstrained motion of the vehicle in some directions.





Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Bobber1]

I have a toyota with a skinny radio antenna. At low speeds, the antenna vibrates in its first mode, swinging to and fro. As I speed up, it will go into its second, then its third mode. I try to get it into higher modes but I can't get the car to go that fast. It's a great teacher.

I once had a jeep ragtop and at speed, the forward portion of the top would lift in the airstream, proving that low-slope windward roofs can experience suction.

Bob

 

[flyby911]

i think the antenna have only one mode like a pendulam (single degree of freedom)