Force transmissibility versus displacement transmissibility

It is well-known that when a single-degree-of-freedom (sdof) system is excited by a continuous motion of the foundation, the force transmissibility, relating the force transmitted to the foundation to the applied force, equals the displacement transmissibility Recent developments in the generalization of the transmissibility to multiple-degree-of-freedom (mdof) systems have shown that similar simple and direct relations between both types of transmissibility do not appear naturally from the definitions, as happens in the sdof case. In this paper, the authors present their studies on the conditions under which it is possible to establish a relation between force transmissibility and displacement transmissibility for mdof systems. As far as the authors are aware, such a relation is not currently found in the literature, which is justified by being based on recent developments in the transmissibility concept for mdof systems. Indeed, it does not appear naturally, but the authors observed that the needed link is present when the displacement transmissibility is obtained between the same coordinates where the applied and reaction forces are considered in the force transmissibility case; this implies that the boundary conditions are not exactly the same and instead follow some rules. This work presents a formal derivation of the explicit relation between the force and displacement transmissibilities for mdof systems, and discusses its potential and limitations. The authors show that it is possible to obtain the displacement transmissibility from measured forces, and the force transmissibility from measured displacements, opening new perspectives, for example, in the identification of applied or transmitted forces. With this novel relation, it becomes possible, for example, to estimate the force transmissibility matrix with the structure off its supports, in free boundary conditions, and without measuring the forces. As far as force identification is concerned, this novel approach significantly decreases the computational effort when compared to conventional approaches, as it requires only local information of the sets of coordinates involved. Numerical simulations and experimental examples are presented and discussed, to illustrate the proposed developments.(C) 2014 Elsevier Ltd. All rights reserved.