Q-Transmissibility Matrix vs. Single Point Transmissibility in Test Environments

Abstract

This paper discusses motion transmissibility concepts and their application to test environments. When a test item is attached to a vehicle at a single point and field external force effects are negligible, test item accelerations can be predicted by using the acceleration transmissibility frequency response functions (FRF) and the test item’s single point field interface motion is used as the input motion. When the test item has multiple interface points and field external force effects are negligible, the motion transmissibility concept is extended by defining a transformation such that the multiple field interface motions can be used as test item inputs in the laboratory. This transformation is defined by the Q-transmissibility matrix that is obtained from the test item driving and transfer point accelerance FRFs and reduces to the standard single point transmissibility FRF for the case of a single interface point. The Q-transmissibility matrix approach is employed to numerically simulated data to predict the test item external motions and it is shown that the usual laboratory setup employing a single vibration exciter and a rigid test fixture leads to incorrect motion predictions and that multiple vibration exciters must be used to simulate field data. Experimental results indicate that: (i) the Q-transmissibility matrix transformation is feasible when dealing with actual data as long as the solution for the test item motions is carried out in a least squares sense since the test item interface FRF matrix may present rank deficiency problems in the solution process, and (ii) Curve fitted accelerance FRFs can be used to reduce experimental noise effects but the quality of the resulting motions is very sensitive to curve fitting errors, especially in the vicinity of natural frequency peaks and antiresonance valleys.