How do you determine the natural frequency of a solid?

[pivoxa15]

All solids have a natural frequency but how do you determine its value?

How would you determine it for a large building?

I'll guess that for each different material they apply a constant external force with a specific angular frequency. The force with an angular frequency that breaks the material will be the natural or reasonant frequency of that material. All the different reasonanct frequencies of different materials are tabulated and the material the building is made out of will determine its reasonant frequency. However buildings with many different materials may be more difficult. Would you just average the reasonant frequencies of the materials?

 

[Tide]

Generally, that is a very complicated problem. Essentially, you write down the equations governing, e.g., the deflection or bending of the structure based on material properties and response to stress and strain. Often that turns out to be a system of coupled oscillators. Analysis of those equations ultimately leads to characterization of the fundamental modes of oscillation.

Also, scale models of the structure are helpful.

 

[FredGarvin]

Actually it's a bit easier than that. The standard is a rap test or plink test. Essentially one uses a hammer or some other object to induce a stepwise input/impulse to the system. That impulse will excite all the modes in the structure at once. Through the use of FFT algorithms, one can see the natural frequencies as spikes in the output. We use this method for determining and verifying the natural frequencies of complex shapes like stator vanes and turbine or compressor blades. However, like you said, these are individual components and not a complex system like a building.

For something like a building, I can't say for sure that it is useful to try to reduce the system down to the overall building has a natural frequency of xxx Hz. I don't think it works like that. They do test buildings in wind tunnels, but I can't say for sure that they can get a resonant response to correlate from the model to the real thing.

 

[pmb_phy]

All solids have a natural frequency but how do you determine its value?

How would you determine it for a large building?

I'll guess that for each different material they apply a constant external force with a specific angular frequency. The force with an angular frequency that breaks the material will be the natural or reasonant frequency of that material. All the different reasonanct frequencies of different materials are tabulated and the material the building is made out of will determine its reasonant frequency. However buildings with many different materials may be more difficult. Would you just average the reasonant frequencies of the materials?

The natural frequencies of something like a solid rod can be determined when the length, Young's modulus for the material and the mass density and, for more complicated systems (such as a pipe, building etc.) the structure. I believe you also need to be more specific in that there are natural freuqencies for both longitudinal and compressional waves which generally have different values. The imnportant thing to know is that there is more than one natural frequency.

A nice text on this topic is Vibrations and Waves by A. P. French.

Pete

 

[gato_]

actually there is not ONE frequency of resonance. In general, a structure can vibrate in different ways. say a rod, for example. A rod can BEND with any substantial stretching. to that degree of freedom, correspond a variety of modes, whose frequency are not multiples of the natural frequency, but there is a fundamental frequency involved. The same rod can stretch along it's axis. Frequencies for this degree of freedom are multiples of a fundamental. In the more general case, there are as many fundamentals as degrees of freedom for one particle (translation, rotation,..). A good first approach is to model things with simple geometries (rods, plates,...) to make an estimation, and then rely on finite elements to obtain an accurate prediction of the modes of a complicated geometry