- [Narrator] In this video we're going to look
at the background to mass participation.
Now we've mentioned previously that
in normal modes analysis we can't calculate
the relative amplitude of each mode.
Simply, each one is a mode shape.
To find a relative amplitude, we're gonna have
to do some kind of response analysis.
Now an exception to this is base motion.
This occurs where the structure
is connected to ground and the ground moves
or shakes and takes the structure with it.
If we assume a unit excitation on the base,
then the term called the modal effect to mass
can be calculated.
Now SolidWorks describes this term as mass participation,
and that's the term we'll be using from now on.
Now the key thing is that mass participation,
or more commonly known as modal effective mass
is actually calculated in the normal modes analysis.
At the top here we see the mass participation table
that can be requested after we run a normal modes analysis.
The structure that the table represents
is the tray which is shown below.
Now mass participation is very useful
for predicting the important modes in response analysis.
For base motion the prediction is exact,
it follows the theory of base motion.
For external loading mass participation gives
a good indication of which modes
are going to be the key players.
Now when we look at the mass participation table
each direction is considered in turn.
So here we're looking at the zed direction,
and if we look at the column the total value is
point nine three two, or 93.2% modal effective mass
or mass participation.
What this means is that 93.2% of the energy
due to the vertical response in the zed direction
is defined by the first 10 modes.
If we look at mode one across the row
we can see it dominates, with a value of 79.3%.
So mode one is a key player, certainly for base motion,
but also very likely for any kind of external loading.
In fact we look at this example under transient loading
and frequency response loading,
and we do in fact find that mode one
is dominant in all cases.
Now if we look at the x and y directions,
first off look in the x direction,
we see the column there.
The total value is only one percent.
Look in the y direction and the total value is
nearly two percent.
So both the x and y directions are unresponsive,
and they may need very high frequency content
to get any response coming out.
In fact there may be no response at reasonable
excitation frequencies in these two directions.
We may have to go up to frequencies which are so high,
they're not really feasible for any normal excitation.
So just summarizing the tray, we went up to 1360 hertz
and there was no significant x or y direction response,
and in the zed direction mode one dominates.
Now by contrast if we look at the beam model,
up to 343 hertz then in this mass participation table
there's no axial response.
Model one is 54% in x, that's a lateral bend one
and mode three is 62% in y, it's a vertical bend one.
In this particular case with the beam,
a higher frequency content is almost certainly needed
so you'd need to run more modes.
So the mass participation challenge is really
to produce a mass participation table
as part of the modal survey and then
estimate the important modes from that table.
From this we can assess whether the level
of participation is reasonable and in particular,
should more modes be included in the response analysis.
Now the number of modes will also depend
on the excitation specification,
and it may be that the specification
cuts you off before you have reached
a significant level of mass participation.
Normally we consider somewhere between 70% or 80%
mass participation is a reasonable number.