23 Predicting System Response at Unmeasured Locations Using a Laboratory Pre-Test 221 23.3 Predictions of Acoustic Test Truth Responses The 2000 Hz frequency bandwidth was divided into 10 equal bands. Each band was analyzed separately. The real part of the FRF matrix and the imaginary part of the FRF matrix from the three reference shakers were stacked side by side. A singular value decomposition of these real numbers was calculated, and the first fifteen orthonormal shape vectors were saved as the Uvectors for each band. Before the estimation process, an algorithm was developed to choose accelerometers to minimize the sum of the condition number for the ten Um matrices. This algorithm reduced the number of maccelerometers to 30 from the initial available 53. Eqs. (23.1) and (23.2) were manipulated to calculate cross spectra in the frequency domain. Fig. 23.3 shows the comparison of the estimated response (red) and the measured acceleration spectral densities (blue) for the 14 “truth” gages. 23.4 Conclusions From previous model validation work [3] it was known that there are at least 70 modes in the 2000 Hz bandwidth. By dividing into bands and using 15 shapes per band, a reasonable estimate of the 14 so called “unmeasured” acoustic test responses was obtained using an optimized set of 30 field measurement gages. Since this approach was an afterthought to the previous work, it is likely that the pre-test could have provided even better basis vectors by attaching more shakers to ensure exciting all possible modes. The advantage of this approach over the finite element approach is that there is great confidence in establishing the basis vectors applicable in each band by the singular value decomposition of the FRF matrix of the asbuilt system. The disadvantage of the experimental-based approach is that only responses instrumented in the pre-test may be predicted, as opposed to the finite element approach, which can at least attempt to predict unmeasured response at any DoF of the finite element model. Notice: This manuscript has been authored by National Technology and Engineering Solutions of Sandia, LLC. under Contract No. DE-NA0003525 with the U.S. Department of Energy/National Nuclear Security Administration. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. References 1. Hall, T.M.: Analytically investigating impedance-matching test fixtures. In: Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Vol. 7, Springer (2019) 2. French, R.M.; Handy, R.; Cooper, H.L.: A comparison of simultaneous and sequential single-axis durability testing. In: Experimental Techniques, pp. 32–37, September/October 2006 (2006) 3. Mayes, R., Ankers, L., Daborn, P.: Predicting system response at unmeasured locations. In: Proceedings of the 37th International Modal Analysis Conference, Orlando, FL, January 2019, paper 4185 (2019) 4. O’Callahan, J., Avitabile, P., Reimer, R.: System Equivalent Reduction Expansion Process (SEREP). In: Proceedings of the 7th International Modal Analysis Conference, Las Vegas, NV, January 1989, pp. 29–37 1989 Randy Mayes has been in the modal testing group at Sandia for 30 years and had some previous experience in finite element modeling.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==