Time-domain analysis of motion transmissibilities in force-driven and displacement-driven structures

A transmissibility is a relationship between signals of the same type, where the input and the output of the transmissibility are outputs of the underlying system. Transmissibility estimates are traditionally obtained using frequency-domain methods, which are based on the assumption that the input and output signals are stationary, and thus initial conditions and transient effects are ignored. In this paper we develop a time-domain framework for SISO and MIMO transmissibilities that accounts for nonzero initial conditions for both force-driven and displacement-driven structures. We show that transmissibilities in force-driven and displacement-driven structures are equal when the locations of the forces and prescribed displacements are identical. We present three examples to illustrate this equality.