Question

I am doing a vibration analysis for a structure that supports two rotating machines. The first machine rotates in a frequency 1911 RPM (T = 0.031397 sec) and the second machine rotates in a frequency 5267 RPM (T = 0.011392 sec). I would like to perform a periodic time history analysis by applying sine and cosine time functions to unit loads in vertical and horizontal directions, respectively, to represent machine loading. However, am not sure what durations should be specified for the time function and for the time history load case (at the same time I understand that for single machine loading the duration of both the time function and the periodic time history load case should be equal to the period of the loading).

Answer

The duration of the time functions representing the loading applied by the two rotating machines and the total duration of the periodic time history load case should be the same as the "common" period of the two machines. This duration could be found as the least common multiple of the two periods. The least common multiple for the two periods of your machines is 60 seconds, which may not be very practical to use because it very long compared to the periods of individual machines and many cycles would need to be included in the loading. It makes more sense to use transient analysis and wait for the transient effects to die out after several cycles of the longer period.

Another possibility is to run separate periodic analyses for the two loads, and then combine them in an additive combination. This would give the max and min response for the sum, but not a step-by-step response. This may be sufficient.