Hi @dkien.mills ,
apologies for delay of my response.
Finally I have found the old example illustrating it which I made years ago.
It was necessary to translate to English the short doc with mathematical/mechanical explanations and comments in the test spreadsheet. All together (example model, doc and spreadsheet) are contained in the first attached ZIP.
This example discusses only the start of machinery and steady state (without stop) and neglects the increase of the amplitude of centrifugal force with the square of rotation frequency.
I have also found the model made several years later, used in the video linked above by @Stephane.kapetanovic
I have attached it to this post too.
Here both start, steady state and stop of machinery are considered, linear change of rotation frequency is assumed during start and stop, and the influence of rotation frequency on the centrifugal force is taken into account.
Unfortunately I have not noted the expressions of forcing functions - but it was easy to derive them again basing on doc I mentioned.
This model contains time history with linear increase of rotation frequency to 10 Hz between 0 and 4 seconds, then constant 10 Hz frequency between 4 and 8 seconds and then linear decrease of rotation frequency from 10 Hz to 0 Hz between 8 and 12 seconds.
Here are the expressions to generate forcing functions for above conditions (for angles expressed in Radians):
"Force FY" excitation in "2_start and stop of rotating machine THA.rtd")
start 0=<t=<4
1/16*t^2*sin(10/4*3.1416*t^2)
steady state 4<t=<8
sin(2*3.1416*10*t)
stop 8<t-<12
-1/16*(t-12)^2*sin(10/4*3.1416*(12-t)^2)
"Force FZ" excitation in "2_start and stop of rotating machine THA.rtd")
start 0=<t=<4
1/16*t^2*cos(10/4*3.1416*t^2)
steady state 4<t=<8
cos(2*3.1416*10*t)
stop 8<t=<12
1/16*(t-12)^2*cos(10/4*3.1416*(12-t)^2)
Regards,
Pawel Pulak
Technical Account Specialist