Figure 1: Subtraction of a fixture (or transmission simulator) from an experimental substructure. The experimental representation of B is obtained by coupling C and a negative modal representation of A (written as B = C-A), which was shown in [2] to cancel the forces exerted by A onto C under certain basic conditions. The uncoupled equation of motion in modal coordinates is given by 2 T 2 2 T 0 0 0 0 C C C C C C A A A A A A q I q f q I q f Z I Z Z I ª º ½ ½ ª º ½ ® ¾ ® ¾ ® ¾ « » « » ¯ ¿ ¬ ¼¯ ¿ ¬ ¼ ¯ ¿ (1) where ZC is a diagonal matrix of nC experimentally derived modal frequencies for component C, and ZA is a diagonal matrix of nA transmission simulator frequencies computed from its FEM model. For either system, I denotes a matrix of mass normalized mode shapes and f the forces applied at the physical coordinates x. It is assumed that the response of component C is measured at nm locations during the vibration test. In order to couple component C and negative component A, the usual approach is to enforce compatible displacements at the interface degrees of freedom. However, in general, it is difficult to place sensors and measure all of the degrees of freedom at the interface, especially the rotations. The next best approach would be to enforce displacement compatibility between the two components at the measured locations, xCm xAm 0 (2) but this leads to several difficulties due to measurement errors at the measurement points. An alternative emerges after transforming to modal coordinates, ICmqC IAmqA 0 (3) Experimental Component: C - = FEM Transmission Simulator: A Experimental Based Component: B 113
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