POLE–ZERO CANCELLATION IN STRUCTURES: REPEATED ROOTS

The conditions for the creation of nodes of normal modes of vibration from the cancellation of poles and zeros are established when either the poles or the zeros (or both) appear as repeated eigenvalues. The analysis is illustrated by numerical examples including the case of a pole–zero cancellation at every co-ordinate at the same frequency which is shown to occur whenever there are repeated poles. If there are repeated poles and repeated zeros at the same frequency then the number of poles must be either one more, one less or equal to the number of zeros.