Natural Frequency Consistent Unit
Natural Frequency Consistent Unit
(OP)
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





RE: Natural Frequency Consistent Unit
MPa = N/mm^2, length = mm, Hz = s^-1 shouldn't have anything to do with density units. Work from there back to mass/volume.
RE: Natural Frequency Consistent Unit
1 N = 1 kg * m/s^2, so there i a connection.
RE: Natural Frequency Consistent Unit
RE: Natural Frequency Consistent Unit
F = m*a
F = Rho*V*a
F = (Tonnes/mm^3)*(mm^3)*(mm/s^2) = (T*mm/s^2) = kg*(1000)*m*(0.001)/s^2 = kg*m/s^2 = N
a = local gravitational acceleration
Rho = density
V = volume
m = mass
To check your time unit (and hence frequency) check the units in:
omega = (1/2*pi)*root(k/m)
pi = 3.1414592 etc
k = stiffness (force/length)
m = mass
Cheers,
-- drej --
RE: Natural Frequency Consistent Unit
For americans working in lbs and feet I'd have no idea what the answer would be.
corus
RE: Natural Frequency Consistent Unit
My recommendation is SI units (or consistent US units).
m, meter is SI (mm is not)
s, seconds
Pa, not MPa
and so on.
The only SI unit with a prefix is kg (kilo is a prefix). There has actually been discussions about renaming kg to something else, just to loose the prefix because it is inconsistent.
Since you are "only" dealing with natural frequencies you can fix the units with resonable effort. When doing transient (time-stepping) or harmonic analysis so the load varies with time (or frequency) you have to be careful with the units. It can be done but SI units always works.
Hence, I use SI units when dealing with dynamics. The only inconvinience are all the digits in Pa instead of MPa but I let the postprocessor handle that, not the solver.
Good Luck
Thomas
RE: Natural Frequency Consistent Unit
Cheers
Greg Locock
RE: Natural Frequency Consistent Unit
A philosophical question, based on your comment that "the choice of units will impact on the numerical accuracy of the solution":
When comparing two terms of a stiffness matrix (or mass matrix, or load vector, or whatever), if one stiffness DOF term is exactly 100,000 times greater than another DOF term when I use SI units (say), won't it still be EXACTLY 100,000 times greater when I use pound/inch units or atomic mass units / cubits, etc? If it is 100,000 times stiffer, it is 100,000 times stiffer.
That is, while I agree that the absolute magnitude of terms can vary enormously, depending on the unit set you select, shouldn't the relative magnitudes be the same in any consistent unit set?
RE: Natural Frequency Consistent Unit
In the mass matrix for a car, in SI the mass will be of the order of 1000 kg, and the moments of inertia will be of the order of 1000 kg m^2, so it'll be a nice matrix to crunch.
In tonne mm, the mass will be about 1, but the moment of inertia will be about 10^6. So you've already lost 5 decimal figures of precision, or about 17 bits.
I must confess I must have the details of this wrong, as this discussion usually results in people recommending tonne mm, not SI!
Cheers
Greg Locock
RE: Natural Frequency Consistent Unit
Not trying to be pedantic (and I could have this totally wrong, anyway!)- but ...
Your maths is fine, but my point is that you don't add the mass terms to the mass-moment-of-inertia terms. Instead, these terms get multiplied by other terms to derive yet further terms. They don't get directly added together (or subtracted from each other) until they have been multiplied by other terms to derive terms with the same units (force, moment, stiffness, displacement, rotation, acceleration, etc). If one force (moment, displacement, ...) is x times bigger than another force (moment, ...) in SI units, it would still be x times bigger in any other consistent unit set.
I thought that when solving matrices, the problem arises when you add or subtract terms of significantly different magnitude, leading to numeric truncation or round-off. Multiplying and dividing terms with very different magnitudes shouldn't directly lead to round-off, as long as the resultant doesn't overflow or underflow the precision of the computer.
You can certainly generate round-off induced problems when the stiffness of adjacent elements is of significantly different magnitude (e.g. joining a very small element directly to a very large element, without a suitable intermediate graded mesh), because the equivalent stiffness terms are directly added and subtracted in the solution process, but the ratio of stiffnesses should be the same whatever unit system you adopt.
Anyway, I might have to have a bit of a think about it!
RE: Natural Frequency Consistent Unit
RE: Natural Frequency Consistent Unit
there are at least a half-dozen versions of SI in use, so why bash customary units. use the units that match the scale of the problem at hand
there is a time and place for rigorous application of SI, beyond that whatever units are convenient justify their use...
RE: Natural Frequency Consistent Unit
You seem to have missed the point. Many, many dynamic and natural frequency calculations over the years have gone wrong simply because the analyst had not used a consistent set of units. The original question of this thread was answered by Drej, but even this consistent set of units has caused confusion. I would always advise anyone to use SI units with modal and dynamic calculations i.e. Newtons, metres, kilograms and seconds, thus ensuring that they are working with a consistent set. What are your other five versions of SI?
RE: Natural Frequency Consistent Unit
You got me a bit confused, half-dozen versions of SI units?? Can you give me two versions and I would be impressed. Note that Pa (pascal) is strictly speaking SI, while MPa is not (M is just a prefix).
The test "constumary" units can also be missleading. Costumary where I work (europe) is SI while in the UK feet etc is sometimes called Imperial units.
Use the units you feel comfortable with but the connection between the units and "the scale of the problem" I don't understand your point. I work with meters, if I work with feet because the design is smaller (problem scaled down) I loose my normal references.
I don't bash "costumary" units but use them either, I've worked with SI since grammer school.
RE: Natural Frequency Consistent Unit
For some preprocessors it's better not to use metres as they have problems dealing with 3 decimal places when your dimensions are only of a few millimetres. There is no problem in using mm as a unit of length providing you use the units of density desribed above. It just takes a little thought.
corus
RE: Natural Frequency Consistent Unit
I understand what you are saying but strictly speaking only meter is base SI unit while "milli" is a prefix, in my opinion that does not mean two versions of the SI system.
I think that is the basic problem in this discussion. That's also what I meant when saying that kg (mass) is in som respects a "problem", it's the only SI unit where the base unit has a prefix. It's no problem to use mm as a length unit but then you have to make sure "your" units are consistent all the way. If you use SI base units the consistency is "automatic".
Say you want to make a thermal analysis. Common unit Watt (W):
1 W = 1 J/s = 1 m^2 * kg * s^(-3). (I picked that from the webpage below.) If you want to the analysis using mm instead of m? Fine, just make sure that you are consistet.
I have seen and heard so many discussions over the years "if I use cm for length, what should I use for mass?" and so on. As for Imperial units I would say that "feet" and "inches" are equally important but, as far as I know, inches are seldom used for length in a dynamic analysis. In stress analysis it is, as you know, much easier to be consistent.
You can find mor information at for example: http://physics.nist.gov/cuu/Units/
Regards
Thomas
RE: Natural Frequency Consistent Unit
RE: Natural Frequency Consistent Unit
There was the old CGS system- centimeter-gram-second.
There are various versions of "the metric system" around. When having the SI system pounded into my head repeatedly in school (20 years ago), it was always impressed upon me how logical it was, how orderly, etc. Then I go to work and discover in the real world, the countries that are "metric" are using stuff like kgf/cm^2. Sheesh.
The basis of the meter was that it was one ten-millionth of the distance from pole to equator. Only it's not exactly, so that leaves it with no real basis.
The standard of mass is the kilogram. Derived by using the units of length and the density of water. Only it SHOULD have been that one cubic meter of water is one gram, rather than than a cubic centimeter. So the logical system loses it's logic. And the standard mass should be a gram, rather than a kilogram.
The unit of temperature measurement SHOULD have been tied to the other units such that heating one gram of water one degree required one joule. Instead, the temperature scale was chosen arbitrarily, and you have to throw in conversion factors there.
And I still don't know what dyne is.
RE: Natural Frequency Consistent Unit
0 degrees Celsius, freezing point for water at sea level.
100 degrees Celsius, boiling point for water at sea level.
And then you have the steps in the scale. Now, strictly speaking Celcius is not SI but for Kelvin the difference is that 0 K is absolute freexing point. That is about -273.15 degrees Celsius. Note that there is no "degrees" Kelvin only Kelvin. Since the steps in Kelvin and Celcius are identical they are often used for the same applications. Farenheit, thats a completely different story.
A question: Do you consider pounds force and kips (kilo pounds) as one or two units? If you consider them as two that would explain to me why you persist in saying there are several SI systems. To me, kilo is a prefix, and they are the same. "milli", "centi" and so on are a concinient way of handling digits, nothing more and nothing less. "kilo" in "kilograms" is another story mentioned in a previous post.
Regards
Thomas
RE: Natural Frequency Consistent Unit
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
RE: Natural Frequency Consistent Unit
RE: Natural Frequency Consistent Unit
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.
RE: Natural Frequency Consistent Unit
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
RE: Natural Frequency Consistent Unit
Regards
Thomas
RE: Natural Frequency Consistent Unit
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.)
RE: Natural Frequency Consistent Unit
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.
RE: Natural Frequency Consistent Unit
Where in the world is it primarily used
Thomas
RE: Natural Frequency Consistent Unit
The F-System is frequently used by foreign freedom fighters in far-flung frontiers of Fiji, Finland and France.
RE: Natural Frequency Consistent Unit
Rob Campbell, PE
Finite Monkeys - www.livejournal.com/users/robcampbell