Publications

In prior work by the author and others [1-3], a new method was demonstrated to extract fixed base modes from a modal test performed on a test article mounted on a vibration slip table. This paper addresses uncertainty that was apparent in frequency and damping estimates in previous work [3]. After reviewing the method based on substructure coupling, additional testing indicates that some of the frequency error was due to different size attachment bolts in the seismic mass truth test and the slip table test. In the previous work, the largest errors in prediction of the truth data were associated with damping. A procedure to subtract significant low frequency slip table damping is implemented and the resulting corrected damping estimate presented. © The Society for Experimental Mechanics, Inc. 2012.

Validation of finite element models using experimental data with unknown boundary conditions proves to be a significant obstacle. For this reason, the boundary conditions of an experiment are often limited to simple approximations such as free or mass loaded. This restriction means that vibration testing and modal analysis testing have typically required separate tests since vibration testing is often conducted on a shaker table with unknown boundary conditions. If modal parameters can be estimated while the test object is attached to a shaker table, it could eliminate the need for a separate modal test and result in a significant time and cost savings. This research focuses on a method to extract fixed base modal parameters for model validation from driven base experimental data. The feasibility of this method was studied on an Unholtz-Dickie T4000 shaker and slip table using a mock payload and compared with results from traditional modal analysis testing methods. © The Society for Experimental Mechanics, Inc. 2012.

Recent advances have provided renewed interest in the topic of experimental dynamic substructures. A focus group has been formed in the Society for Experimental Mechanics to advance the experimental dynamic substructures technology and theory. Sandia National Laboratories has developed two identical test beds to enable the focus group to advance the work. The system chosen was an Ampair 600 wind turbine with a fabricated tower and base. Some modifications were made to the system to make it more linear for initial studies. The test bed will be available for viewing in the technology booth of the IMAC exposition. A description of the turbine and modifications will be presented. Initial measurements on the full system will be described. Initial modal tests have been performed on six blades at the University of Massachusetts at Lowell [1]. Geometry and mass measurements for finite element modeling have been performed by the Atomic Weapons Establishment in the UK [2]. Initial efforts to quantify each blade as an experimental substructure are ongoing. One goal is to develop an experimental dynamic substructure of the blades and hub to couple with a finite element model of the nacelle and tower to predict parked system response. © The Society for Experimental Mechanics, Inc. 2012.

The transmission simulator method of experimental dynamic substructuring captures the interface forces and motions through a fixture called a transmission simulator. The transmission simulator method avoids the need to measure connection point rotations and enriches the modal basis of the substructure model. The free modes of the experimental substructure mounted to the transmission simulator are measured. The finite element model of the transmission simulator is used to couple the experimental substructure to another substructure and to subtract the transmission simulator. However, in several cases the process of subtracting the transmission simulator has introduced an indefinite mass matrix for the experimental substructure. The authors previously developed metrics that could be used to identify which modes of the experimental model led to the indefinite mass matrix. A method is developed that utilizes those metrics with a sensitivity analysis to adjust the transmission simulator mass matrix so that the subtraction does not produce an indefinite mass matrix. A second method produces a positive definite mass matrix by adding a small amount of mass to the indefinite mass matrix. Both analytical and experimental examples are described. © The Society for Experimental Mechanics, Inc. 2012.

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Qualification vibration tests are routinely performed on prototype hardware. Model validation cannot generally be done from the qualification vibration test because of multiple uncertainties, particularly the uncertainty of the boundary condition. These uncertainties can have a dramatic effect on the modal parameters extracted from the data. It would be valuable if one could extract a modal model of the test article with a known boundary condition from the qualification vibration test. This work addresses an attempt to extract fixed base modes on a 1.2 meter tall test article in a random vibration test on a 1.07 meter long slip table. The slip table was supported by an oil film on a granite block and driven by a 111,000 Newton shaker, hereinafter denoted as the big shaker. This approach requires obtaining dominant characteristic shapes of the bare table. A vibration test on the full system is performed. The characteristic table generalized coordinates are constrained to zero to obtain fixed base results. Results determined the first three fixed base bending mode frequencies excited by the shaker within four percent. A stick-slip nonlinearity in the shaker system had a negative effect on the final damping ratios producing large errors. An alternative approach to extracting the modal parameters directly from transmissibilities proved to be more accurate. Even after accounting for distortion due to the Harm window, it appears that dissipation physics in the bare shaker table provide additional damping beyond the true fixed base damping.

Recently, a new substructure coupling/uncoupling approach has been introduced, called Modal Constraints for Fixture and Subsystem (MCFS) [Allen, Mayes, & Bergman, Journal of Sound and Vibration, vol. 329, 2010]. This method reduces ill-conditioning by imposing constraints on substructure modal coordinates instead of the physical interface coordinates. The experimental substructure is tested in a free-free configuration, and the interface is exercised by attaching a flexible fixture. An analytical representation of the fixture is then used to subtract its effects in order to create an experimental model for the subcomponent of interest. However, it has been observed that indefinite mass and stiffness matrices can be obtained for the experimental substructure in some situations. This paper presents two simple metrics that can be used by the analyst to determine the cause of indefinite mass or stiffness matrices after substructure uncoupling. The metrics rank the experimental and fixture modes based upon their contribution to offending negative eigenvalues. Once the troublesome modes have been identified, they can be inspected and often reveal why the mass has become negative. Two examples are presented to demonstrate the metrics and to illustrate the physical phenomena that they reveal.

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This work presents time-frequency signal processing methods for detecting and characterizing nonlinearity in transient response measurements. The methods are intended for systems whose response becomes increasingly linear as the response amplitude decays. The discrete Fourier transform of the response data is found with various sections of the initial response set to zero. These frequency responses, dubbed zeroed early-time fast Fourier transforms (ZEFFTs), acquire the usual shape of linear frequency response functions (FRFs) as more of the initial nonlinear response is nullified. Hence, nonlinearity is evidenced by a qualitative change in the shape of the ZEFFT as the length of the initial nullified section is varied. These spectra are shown to be sensitive to nonlinearity, revealing its presence even if it is active in only the first few cycles of a response, as may be the case with macro-slip in mechanical joints. They also give insight into the character of the nonlinearity, potentially revealing nonlinear energy transfer between modes or the modal amplitudes below which a system behaves linearly. In some cases one can identify a linear model from the late time, linear response, and use it to reconstruct the response that the system would have executed at previous times if it had been linear. This gives an indication of the severity of the nonlinearity and its effect on the measured response. The methods are demonstrated on both analytical and experimental data from systems with slip and impact nonlinearities. © 2010 Elsevier Ltd. All rights reserved.

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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.

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