Understanding Transmissibility Properties

The dynamic response of a structure is often studied based on the measurement of frequency response functions, which may or may not pass through an identification process in order to build a theoretical model, which mimics, as truthfully as possible, its real behaviour. Sometimes it may also be important to understand, for a given set of applied forces, how two sets of dynamic responses relate to each other, namely when one of them is unknown. This represents a different way of quantifying the dynamic behaviour of a structure. Such a relationship between two sets of responses is traditionally called transmissibility. It is presented in every basic vibration textbook for the single degree-of-freedom system. The extension to a general multiple degree-of-freedom system was proposed some years ago and since then various papers have been written, developing the subject in several ways. However, some issues have not been well understood, like the nature of the transmissibility curves themselves and the potentialities of other properties and relationships. The objective of this paper is to clarify and explore those properties. The developments will be illustrated through some simple numerical examples, aiming to simulate experimental data.