Zeros of a transfer function in a structural vibrating system

Abstract

This paper analyzes a transfer function (TF) of a structural vibrating system in the complex‐frequency domain based on wave 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. These zeros mentioned 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. 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 three‐dimensional space vibration. The truncation effects of an impulse response on the zeros are also mentioned.