Publications
Extracting fixed base modal models from vibration tests on flexible tables
Traditionally modal and vibration tests have been performed separately because their classical purposes require different inputs and outputs. However, motivation exists in some instances to be able to perform a modal test on a shaker table, if the boundary conditions could be accounted for appropriately. This is especially a concern for large test articles mounted on large tables because the table has flexible dynamics in the frequency range of interest for the modal test. For the past thirty years various attempts have been made to develop a method that would allow the two tests to both be conducted on a shaker table requiring only one setup. However, in most cases the table is assumed to be rigid. When the table cannot be assumed rigid the remaining approaches usually require that all six forces and all six degrees of freedom of motion at every attachment points be measured. Most approaches neglect moments and rotation measurements. Even measuring the translational forces and accelerations is rarely done. In the method employed here, the boundary condition is constrained mathematically. However, a measure of the shaker force is required. In addition, the classical mathematical constraints to produce a fixed base result are augmented in a way that alleviates the ill conditioning that almost always results when using the classical constraint equations. The two major advances here are a method to estimate the shaker force, and improved conditioning of the constrained equations. The effect of improving the conditioning is demonstrated with a modal test of hardware on a base that is not fixed. The full process is demonstrated with a random vibration test on a simple flexible horizontal slip table with a cantilevered beam mounted as the test article. A general outline of the method proceeds as follows: 1) characterize the modes of the bare shaker table attached to the shaker; 2) mount and instrument the test article; 3) attach a portable shaker to the tip of the shaker table with a force gage and measure a specific frequency response function (FRF); 4) detach the portable shaker and run the typical random vibration test; 5) calculate transmissibilities to the tip accelerometer; 6) create acceleration/force FRFs from reciprocity by multiplying the FRF in step 3 times every transmissibility; 7) extract modal parameters from FRFs; 8) finally apply augmented constraint equations with FRFs synthesized from the modal parameters and extract the fixed base modes. © 2009 Society for Experimental Mechanics Inc.