- [Instructor] In this video,
we're going to review pre-stiffened normal modes analysis.
Now, many real-world components
are subject to some kind of pre-load,
or they might develop steady state loads
during their operation.
For example, we've got pre-tensioned bolts.
Imagine a transmission tower which is braced to ground
by heavily pre-stressed guide wires.
And a helicopter rotor blade when spinning
has a tremendous level of centrifugal force
which really stiffens that blade up.
That's the example we're gonna be using
in our demonstration video
which is coming up shortly.
Now, the pre-stiffening effect,
and if we look at the helicopter blade here as an example,
it's spinning about the spin axis,
it develops a very high load within the structure.
The linear stiffness matrix that we calculate
is unaffected by this,
so we'd call that linear stiffness matrix.
But then we have a load dependent stiffness matrix,
and that's actually changing.
So that's the stiffness matrix dependent
on the loads which are developed.
As the tension increases,
then that stiffness matrix will increase its value.
As the tension decreases
and the props goes into compression,
then that will reduce the stiffness,
but there's a possibility that buckling may occur
before we get down to low frequencies.
The mass matrix, in the meantime, is unaffected.
So our revised equation of motion,
and now our combined stiffness matrix,
K linear plus K load dependent,
is the total term we use in the argument value
extraction calculation.
The interface within SOLIDWORKS,
the static load is defined with no time dependency.
This is defined within a normal modes analysis.
So in this particular case,
it's the centrifugal loading of 220 RPM.
The fixtures or constraints are applied as usual,
and then the frequency or the normal modes analysis
is run as normal.
Now there is one thing to look out for there.
We have to use the sparse solver.
If we don't,
then we'll get an error message coming out there.
So in summary,
it's pretty easy to set up
a pre-stiffened normal modes analysis inside SOLIDWORKS.