- [Instructor] In this video,
we look at the background to frequency response analysis.
This is a general background,
and I relate frequency response analysis
and compare it to transient analysis.
Then I look at the input requirements
for frequency response.
Now these are very specific
and need controlling very carefully.
And then I look at the output responses
coming from the frequency response analysis.
So the first question is, what is frequency response?
Well many loading environments have very strong
and sustained periodic content or periodic input.
Now this input could have a constant amplitude and phase
across a frequency range,
and that would be something like
a shaker table or an exciter,
or the amplitude and phase may vary,
something like a rotating system, vortex shedding,
or driving across road surfaces.
The objective of frequency response analysis
is to investigate the steady state response
across a frequency range, to input of this periodic type.
Now each specific input frequency point
across a frequency input range represents a harmonic input.
That means it's a steady state oscillating input
at that specific frequency.
We need to define the magnitude of the input,
we need to define the relative phasing of the input,
and we've already defined the frequency of that input.
The input can be loading or enforced motion,
it can be an external load, like an external strike or hit,
or it could be a base motion.
To understand what frequency response is doing,
it's quite useful to compare it to a transient analysis.
So we've got a little two-degree-of-freedom example here.
There's a steady state oscillating input,
the transient input function is amplitude one,
and then sine omega one times t.
Omega one is the input or driving frequency.
So the single frequency, magnitude of one
and phase of zero, have been defined.
Now if we look at the response through time
of those two degrees of freedom,
we see a larger response and a smaller response,
in terms of amplitude.
Now the initial response is called a transitory response
and it's building until it balances
energy dissipated by damping
equals energy pumped in by the oscillating input.
And at that point, it's reached a flat,
steady state response.
So we could investigate a series of inputs,
where we change the frequency and change the magnitude,
but we need a transient analysis for every frequency input,
and that would be very inefficient to do that.
Now if we're only interested in the steady state response,
then we can use a frequency response analysis instead.
So here's the frequency response setup.
We're exciting at the same degree of freedom
as we did previously in the transient,
but we're sweeping across a range of frequencies.
At every point of our input,
we're assuming a steady state oscillating input,
the magnitude and phase of that input
have been defined for all the frequencies.
And as I mentioned,
here it's just a straightforward constant input.
Now the frequency response ignores the transitory period
and it calculates only the steady state response.
So if that's what we're interested in,
then this is a perfect application.
The frequency response will give exactly
the same amplitudes as the transient, at the steady state,
for the oscillating input specified.
The main difference then is that frequency response analysis
covers a very wide frequency envelope.
It's very much cheaper to do that type
of steady state analysis
than do a whole series of transients.
So if we're looking for an envelope,
looking for sensitivity across a frequency range,
then we use a frequency response analysis.
Now the input into a frequency response in SOLIDWORKS
can be defined in one of two ways.
We can have a constant input,
which is just a single magnitude and phase
across a frequency input range.
That's very simple to define,
and it's often described as a sine sweep,
somewhat similar to what happens on a shaker table.
There's a straight sweep through, a constant acceleration,
or a constant input force.
The alternative form of input is a curve,
which varies magnitude and phase
across a frequency input range,
and that's a user-defined curve.
And this represents a specification,
where the client or the certification authority
has said this envelope represents
a typical frequency response input
that our component is going to see.
One little catch in SOLIDWORKS is that the range definition
in the user-defined curve, the upper and lower bound,
must match the analysis range that's defined
on the frequency to response analysis properties.
Now frequency response calculation points
are very important for accuracy.
Here's part of a frequency response curve,
where we can see two actual frequencies
in a frequency response.
Now I've described these as the peaks,
and we must have a point for each natural frequency,
we must hit that natural frequency exactly right,
what I'm calling a peak.
Now SOLIDWORKS does a good job for us here,
because it's a modal-based technique,
it knows what the natural frequencies are.
And a point is guaranteed at those positions.
We also want to have a good spread around each peak,
so that the shape of the curve around the peak
is captured very well.
Again, SOLIDWORKS gives us some useful controls here.
The final thing we have to look out for
is a good spread between the peaks, what I call the valleys.
Now this isn't really automated,
so you may have to juggle a little bit with the inputs,
to make sure you do pick up
a nice, smooth shape through that valley.
Capturing the overall shape
of the response curve is important.
If we're going on to do a random response analysis,
for example, then it becomes absolutely vital
to get a good shape, because we're gonna be using the area
underneath the frequency response curve.
So the setup of calculation points in SOLIDWORKS
is actually very straightforward.
As I mentioned, it uses a modal method,
so it's already calculated the natural frequencies,
it's already hit the peaks.
So the two stages are, first off, the normal modes analysis
and then the frequency response analysis.
Now in practice,
if you're running a frequency response analysis,
you can either do this in two steps or you can just
go straight for the frequency response analysis
and it will automatically do
the normal modes analysis as well.
As I mentioned, the modal method ensures
that we capture those peaks.
The spread is controlled by the number of points,
the bandwidth, and the type of interpolation,
either linear or logarithmic.
The spread and the valleys may need some juggling
on the bandwidth control.
It's quite normal to run a few times,
experimenting with settings there
before you get the nice, smooth curve
that you're happy with.
In summary, the SOLIDWORKS setup
for frequency response calculation points
is very straightforward, but even so,
there's some juggling required
and the implications of the controls are important.
So what I'd recommend is some experimentation
with fairly simple models.