The global transfer direct transfer method applied to a finite simply supported elastic beam

The Global Transfer Direct Transfer (GTDT) method is a two-step transmission path analysis method. It is used to analyze the signal transmission among subsystems from a general N-dimensional linear network, representing the physical model under study. In the first step, the Global Transfer Functions (GTFs) are measured and the Direct Transfer Functions (DTFs) are calculated from them. In the second step, the signal vector is measured for the network running under the desired operational conditions. It is then possible to reconstruct the signal in any subsystem from the contributions of all other subsystems plus its own external excitation. This is done by means of the previously calculated DTFs. This paper is intended to clarify how the GTDT method works. This is done by means of an analytic study of the bending wave transmission between three points in a finite simply supported elastic beam. This problem constitutes a particular four-dimensional example of the general N-dimensional network. Concerning the first step of the method, special emphasis is given to the relationship among the DTFs and the GTFs, as well as to elucidate the role of the DTF matrix as a connectivity matrix. As for the second step of the method, the particular case of a correlated force vector acting on the beam is addressed. It is shown how the signal at any subsystem can be reconstructed from the signals at all the other subsystems. In practical implementations this allows to identify problematic subsystems in order to perform appropriate design modifications and avoids the necessity of having to measure operational forces.