34 A Comparison of Different Boundary Condition Correction Methods 327 34.4 Method 1: Fixed Base Correction Method The fixed base correction method (FBCM) directly calculates FB FRFs from the test data by using base acceleration data or constraint shapes as references in either the initial calculation of the FRF matrix utilizing the Hd method [16], or through a partial matrix inversion of the FRF matrix with the structural modification using frequency response functions method (SMURF). For this work, constraint shapes [ ] were calculated and used as the references. The constraint shapes relate the baseDOFs {xB} to a set of DOFs associated with each constraint shape, : {xB}=[ ] { } (34.1) The measured FRF matrix that contains the TA{xI} and base DOFs can be back-expanded to include the DOFs associated with each constraint shape: xI xB = HII HIB HBI HBB fI fB → xI = HII HIB +HBI +HBB fI fB (34.2) A partial matrix inversion of the FRF matrix can be performed to utilize the constraint shape DOFs as references to remove the base motion of the interface and obtain the FB FRFs: fB =− +HBB T +HBIfI + +HBB T (34.3) The resulting FRF matrix relation is as follows: xI xB = HII −HIB +HBB T HBI HIB +HBB T HBI −HBB +HBB T +HBI HBB +HBB T fI (34.4) The constraint shapes were calculated from a singular value decomposition (SVD) of the FRF matrix partitioned down to the 45 base DOFs. To calculate the FB FRFs, the SMURF method was used to invert all the impacts on the base, with eight constraint shapes encompassing the six rigid body modes and two flexible plate modes. The eight constraint shapes encompassed 93% of the total baseplate motion. Figure 34.6 contains a CMIF of the FB FRFs for only the response DOFs Fig. 34.6 CMIF of FB FRFs with only flange and cylinder response DOFs and cylinder impacts as references
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