Modal Truncation (cont’d)

In addition to FD - FU ?? F'D-F'U one must also recognize that if FD and FU are not full rank then:

(FD-FU) L = 0

may be satisfied because

FDL ? FUL ? 0

Namely the vector in L is the common null space of FD and FU (unidentified modes which do not change due to damage)

In Summary
• Unidentified modes that do not change do not affect the accuracy of the vectors in L but introduce vectors that are not DLVs
  (one must have a means to exclude them)
• Unidentified modes that do change affect the accuracy of L

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