THE TRANSMISSIBILITY CONCEPT IN MULTI-DEGREE-OF-FREEDOM SYSTEMS

A generalisation of the transmissibility concept to multi-degree-of-freedom systems is presented. A transmissibility matrix between two sets of response functions of a structure is built in either of two ways: (i) from the mobility matrices of the structure or (ii) from test-measured responses only. In a typical case, the known (or measured) responses constitute one of the sets, while the other set includes the responses at any other co-ordinate. It is shown that the transmissibility is, in general, a rectangular matrix, since the number of response functions in each of the sets need not be the same. Nevertheless, to allow for a solution for the unknown responses, the number of the known responses needs to be at least the same as the number of generalised forces applied to the structure. Some practical applications are addressed, either in predicting the response at points where no transducers are allowed in field service or in damage detection. Also, some properties are presented and explained, namely the validity of the transmissibility for grounded structures and the existence of an inverse transmissibility matrix.