How is vibration analysis done for two machines which rotate at different frequencies?
Extended Question: I would like to perform the periodic time-history analysis of a structure which supports two rotating machines which operate at different frequencies (1911 and 5267RPM, T = 0.0314 and 0.0114sec). Sine and cosine time functions are applied to unit loads, in both the vertical and horizontal directions, to simulate machine loading. What duration should be specified for the time function and the time-history load case? I understand that these values should be equal to the period of loading for a single machine, but how is analysis implemented for two machines?
Answer: The duration of the time functions which represent the applied loading from 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 may be found as the least common multiple of the two periods. In this case, the least common multiple is 60 seconds, which may not be practical since this duration is long relative to the operating periods, and would require inclusion of many cycles within the loading condition. A more practical application may be transient analysis, in which time should be taken for the transient effects to subside after several cycles of the longer period.
Another option is to run separate periodic analyses for each load, then combine their response within an additive load combination. Maximum and minimum response would be reported for the sum, but not step-by-step response.