How can I get around the 1000 mode limit in a spectrum analysis?
Can I run the spectrum analysis in segments?

Yes, you could do a spectrum in segments. The participation factor
of each mode is independent of the other modes that are used.
If you are using the SRSS combination technique, the segment
results can be SRSS'd together using LCOPER,SRSS in POST1.

If you are using a method like GRP or CQC, solving in segments
does lose the modal interaction between the modes near the cut-off
frequency. I think this would be a small error, though.

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