Natural Frequency and Dynamic response

[sybie99]

Hi

I am trying to get a better understanding of dynamics of structures. I have read quite a few books on the subject but cannot seem to get a simple explanation to what I am trying to understand.

If say I have a steel structure, say a free standing staircase 15metres high exposed to lateral windloads. I know how to use software to calculate the modal shapes with their frequencies. I also know the horizontal deflections due to wind. What I am trying to find out is whether the structure will ossilate. How do I calculate the frequency of the wind loading on the structure? Is this where the dynamic response comes into play? I am not quite sure how response is calculated or measured, or in fact exactly what is meant by response. I have heard the term dynamic response and response factor.Is this needed in checking a structure for vibration?

Is there a simple way for me to calculate whether the structure will "vibrate" or vibrate at an acceptable frequency?

I know this is a very complex topic, but maybe there is someone out there who can out it into simple terms.

Thaanks for your help guys

 

[larsacious]

sybie99:

I believe you are confusing 2 possible scenarios. One scenario is wind vortex shedding which causes the structure to vibrate. The second scenario is when the structure's natural frequency matches the applied load's natural frequency (called resonance). The first scenario is more common to single pole arms (light poles, sign supports, etc) and is a phenomenon that occurs due to wind or fluid motion. The second scenario would more likely be caused by an earthquake motion that would match the stair case structure's natural frequency (unlikely) and cause a resonance situation in which the structure would deflect more and more with each cycle.

With this being said, I doubt your stair case will have any wind induced vibrations that will effect the structure globally. The dynamic response factor (used in ASCE 7) is used for earthquake design and is based on the type of structure and it's dynamic performance.

Hope this makes some sense.

Ryan

 

[lutein]

with my limited vibration experience, here are the several vibrations you may be looking at:
1. walking vibration from long span. this could be estimated easily by using AISC Design Guide series 11.
2. 2 types of possible wind vibration for stairs:
a) vortex shedding
if you have a flat and wide stairs, vortex should not govern, see ASME STS-1-2006 Section 5.2.2 for formulas to determine the possiblity of vortex shedding.

b) fluttering
if you have a relatively long span x wide span x flat structure, fluttering will most likely happen in lieu of vortex shedding. I dont have a good design guide for this.

 

[chris9]

A good place to start is to first of all determine your operating frequency range in Hz. This could be due to any external pulsating force such as earthquate etc. Then check the mode frequencies of your structure within your operating frequency range. If any of the modes are within your operating range this means the structure may resonate (vibrate) at that frequency. In an ideal world you would prefer not to have any modes within your operating range.

If you have modes in your operating range you can perform more detailed analysis such harmonic reponse etc. You can find stress and displacement from this type of analysis.

Chris

http://www.value-design-consulting.co.uk