5 Vibration Test Design with Integrated Shaker Electro-Mechanical Models 71 0 500 1000 1500 2000 Frequency [Hz] 10-4 10-2 100 102 H a/e FRF [(m/s2)/V] Test Model 0 500 1000 1500 2000 Frequency [Hz] 10-4 10-2 100 102 104 H a/i FRF [(m/s2)/Amp] Test Model Fig. 5.11 Acceleration/voltage (left) and acceleration/current (right) FRFs of the substructured model compared with the measurement Fig. 5.12 Candidate shaker locations on the DUT model (left) and chosen locations for six shakers based on the coupled DUT-shaker model predictions (right) can be extracted from the FE model. There are axial-direction inputs at the top and bottom, and radial-direction inputs on discs and transverse inputs on the base. The objective is to determine the locations of six shakers to achieve response of the DUT measured at those 33 response DOF in some previously-measured field environment. This is essentially a 33 output, 6 input multiple-input/multiple-output input estimation problem. The first step in that input estimation problem is determining the locations of those 6 inputs from the 37 candidate locations, which is where connecting the shaker model to the DUT model with FBS comes in. Inputs and responses will be predicted given a set of 6 shaker locations sampled from all combinations of 6 locations in 37 candidates. Then, the results for different input locations will be compared in terms of the response accuracy and required input levels. Any input locations which require too much input, in terms of force or current, will be omitted. The locations which provide the best response accuracy within the capabilities of the shaker will be chosen for a future multi-shaker experiment of this DUT. Results of the evaluation of a random set of 2000 of the 2.3 million possible location combinations yields predictions of the response accuracy, and the shaker force, current, and voltage. These predictions are the in the form of CPSD matrices, which results in far too much data to easily view and interpret. Instead, the predictions are condensed down over the frequency band in terms of the root mean square (RMS) response error, shaker force, current, and voltage. Then, those RMS values are condensed down over the gauges or shakers by taking a mean of the RMS values. This results in a single scalar value for each parameter for each set of shaker locations. These condensed results can then be viewed in terms of their distributions to
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