Holding A Tune with SOLIDWORKS Simulation
In this blog we’re going to
have a look at modelling a simplified guitar string and seeing the effect of
stretching the geometry, in the way of using a prescribed displacement, has on
the first natural frequency of the guitar string using a SOLIDWORKS Frequency
We’re going to assume that the
guitar string is 0.6m long, has a cross section diameter of 0.5mm and is made
from Alloy Steel, which has the material properties:
Density: 7700 Kg/m3
The setup being used in this
study is a solid mesh (as beam meshes do not allow the Prescribed Displacement
External Load) of curvature based, high quality elements of default size. One
end is fixed (which therefore has all 6 Degrees of Freedom fixed), whilst the
other has a prescribed displacement normal to the end face of the guitar
string, with the other two translation directions fixed.
In this study we’re going to
look at the first natural frequencies using displacements in the Z-direction of
1 to 10mm in increments of 1mm. To do this we’re going to use a Design Study.
To start this design study we first need a variable, which in this case is the
Prescribed Displacement. So by editing the Prescribed Displacement in the
frequency study, going to the Z-translation, clicking the dropdown arrow and
selecting link value, we will be able to create a variable.
The pop up window will be
empty as we will not have created any variables yet. Clicking on
“Edit/Define..” opens up a new pop up window which allows us to create the
simulation variable we require.
Using the settings from the
screengrab above we can then hit “Apply” and “Ok” which will close the pop up
window and take us to the previous pop up. In this window we just need to
select the variable we created, in this case it is called “Displacement” and
then hit “Ok”. Once this is done, the variable is now linked to the Prescribed
Displacement in the frequency study which we can then alter in the Design
Study. The value box for the Z-translation will now have turned grey to
indicate that it is linked. To create the study simply right click on the
frequency study just above the Status Bar and select “Create New Design Study”
Going into the Design Study 1
tab we can then create our Design Study. In the variables we are going to
select “Displacement” from the drop down menu, using “Range with Step” option
going from 1mm to 10mm with 1mm steps. In the Constraints options we’re going
to select “Add Sensor…” from the drop down menu and create a sensor which will
get the value for the first natural frequency value.
And we will then set this
Constraint, “Frequency1”, to Monitor only. All we need to do now is clear the
optimization checkbox by the Run button and hit Run. This will automatically
run all 10 simulations for us and give us the results.
Therefore, as we tighten the
guitar string and increase its length, the natural frequency increases. This
blog was done on a simplified guitar string, but in reality guitar strings
increase in length and diameter. Using the design study, creating a few more
variables and linking them to the model you would be able to test all 6 real
guitar strings and see how much you have to tighten it to get the correct
frequency out. The setup of the geometry, frequency study and design study all
took under 10 minutes with another 5-10 minute run time. This really quick
simulation has given us a lot of data which you wouldn’t be able to work out
any other way than real life testing, which takes a lot longer!
By Chris Boyles