The quaterninon transmissibility

This paper developed the common transmissibility to a quaternion form. The quaternion transmissibility was calculated based on the time-domain sequences of spatial vibration signals by using technique of quaternion Fourier transforms (DQFT). The quaternion transmissibility is superior to the common one because it can be used to deal with the spatial vibrations that are composed from three directional synchronous vibrations. And compared with the common transmissibility, the modular vector of the quaternion transmissibility is consistent with its theoretical value in spite of the installation orientation of the sensors, which is important in engineering applications of the transmissibility such as the structural damage identification. An actual damage identification experiment was carried out to verify the availability of the quaternion transmissibility, where technique of the Karhunen-Loeve Transform (K-LT) was employed. The identification results based on both common and quaternion transmissibility were obtained and compared with each other.