Zeros of a transfer function in a multi-degree-of-freedom vibrating system

This paper analyzes a transfer function (TF) of a vibrating system in the complex-frequency domain based on modal theory. There are three cases of zeros in a TF. One is the usual case where a zero is located on the pole line connecting two adjacent poles. Another is the double-zero case; that is, there are two zeros on the pole line between two adjacent poles. Those zeros above are minimum-phase zeros. The third case, however, can contain a nonminimum-phase zero. A pair of minimum- and nonminimum-phase zeros is located symmetrically with respect to each other at equal distances from the pole line because the transfer function has a symmetrical form in a complex domain with respect to the pole line, assuming real residues (i.e., real mode shape functions). One member of this pair of zeros can be a nonminimum-phase zero, under the condition that the damping is small. Such zeros have been numerically confirmed using the TF of a rectangular room.