Natural Frequency Consistent Unit 6

[Eser]

Hi Everbody!

I have a general question about dynamic analysis. If we want to have the natural frequency in Hz and we have the distances in mm and the Young modulus in MPa what should be the consistent unit of material densities?

Thanks in advance,

Eser

 

[hacksaw]

whoa, i did not expect such a response

i should have said "metric" rather than SI. true SI discourages the use of mm or cm in lieu of meters, yet acknowledges that "nm" are okay. it is no better than any of the other systems in that regard.

in the real world, you have pressure units of kilponds/cm2, kg/cm2, kg/mm2, Pa, Bar, Atm, mmHg, mmWC(water column),for example. these are used because they are meaningful to the application at hand

when it comes to piping design, you discover that mm are commonly used for pipe diameter, not cm or m. these are not just ordinary mm dimensions, they are "nominal", because the pipe is, in many cases, manufactured in inches,

unless you are using DIN or JIS piping standards, in which case you have a whole new set of problems.

The units for vibrating systems is no less confusing with the elastic and shear moduli expressed as kilponds/cm2, kg/cm2, kg/mm2, Pa, but with much of the testing data in various metric and SI units, and even customary english units.

SI is great in a perfect world

 

[UcfSE]

The meter is now defined as the distance a certain frequency of light emitted from such and such a sourse travels in a defined amount of time.

 

[JStephen]

ThomasH, the temperature scale IS arbitrary. For example, I recall that Fahrenheit's scale used human body temperature as 100 and the coldest mixture of ice and salt he could get as zero. That makes just as much sense as setting the boil/freezing temps to arbitrary numbers. The Celsius scale could just as easily have set freezing at 100 and boiling at 1000, for example, or at zero and 1, that would be just as "metric" as the current system. The catch is the size of the units wasn't tied in to any other physical constant, like it could have been. In the english system, the heat unit (BTU) is tied to the temperature scale (as is the calory), but then you have a conversion factor between that unit and the force x distance energy units.

UcfSE, I realize the definition of the meter. But it is still an arbitrary definition- it's simply a more definite definition of the same meter. For example, it's some odd number of those light wavelengths...not 10^8 or something.

 

[ThomasH]

This discussion got more intersting than I first expected.

hacksaw:

I would say that the most important thing about units are that you should be consistent, and comportable. If you are more comfortable with kiloponds/cm^2 then MPa, fine. But I would not say that kiloponds/cm^2 is "real world" while MPa i someting else.

JStephen:

OK, the temperature scale can be seen as arbitrari in the sense that it is defined by man.
Now the base SI units are:

length, meter, m
mass, kilogram, kg
time, second, s
electric current, ampere, A
thermodynamic temperature, kelvin, K
amount of substance, mole, mol
luminous intensity, candela, cd

Aren't they all in a sense arbitrari, that is defined based on something or other. There are also a lot of derived units such as Joule, 1 J = 1 N m = m^2 kg s^(-2). Now if the meter is arbitrary, doesn't that make the Joule and the rest of the SI system equally arbitrari? And isn't the Imperial system equally arbitrary, or is a foot a better basis than some fraction of the distance between the equator and the pole. Does the system get better because the definitions are less abstract?

My recommendation is always: use the units you feel comfortable with, and make sure you are consistent. For stress analysis it's easy, for dynamics a bit more complicated but do'able.

Regards

Thomas

 

[ThomasH]

Sorry, what I meant in my previous post is that all units are arbitrary in the sense that they are defined by man, not nature. Or am I wrong in this assumption?

Regards

Thomas

 

[jhardy1]

It always amuses me how much trouble some people seem to have when it comes to defining a consistent set of units for dynamic analysis etc. While I have always found using basic SI units to be pretty simple and just about foolproof, I just came across the following truly elegant alternative – the so-called “F-System”:

In the F-system, we adopt the (relatively) common units of time, the fortnight (ft), and length, the furlong (fl). Now, to get consistent units of force and mass, we use two electrical units, the farad (f) and the Faraday (F). The resulting unit of current is the Faraday/fortnight (F/ft), and the unit of potential difference is the Faraday/farad (F/f). Thus, the unit of power is the square Faraday per farad per fortnight (F^2/(f ft)), and the unit of energy is the square Faraday per farad (F^2/f). Finally, the unit of mass is, of course, (F^2 ft^2)/(f fl^2), or square Faradays square fortnights per square furlong farad. (This unit is about 2.3 atto kg, in case you were wondering.)

 

[johnhors]

Julian

You left one of the F units out, the British Standard Ferkin, which usually occurs in pairs, as in two ferkin long, two ferkin high, two ferkin short and so on.

 

[ThomasH]

I thought that I had seen the various unit systems that are used but F-system is definitly a new one.

Where in the world is it primarily used ;-)?

Thomas

 

[jhardy1]

ThomasH,

The F-System is frequently used by foreign freedom fighters in far-flung frontiers of Fiji, Finland and France.

 

[imagitec]

Usually, by this point in the thread, someone has pointed out the innate superiority of the Imperial system because the units of length were originally derived from body parts. Thus, working in Imperial units gives ua a better intuitive sense of the problem. Many a time I have been stymied by a difficult problem, only to think, "Wait a minute. This is all just so many thumbs and elbows. I can figure this out." And like a morning dove through an open window, the answer comes to me.

Rob Campbell, PE
Finite Monkeys -

http://www.livejournal.com/users/robcampbell