Publications

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This paper presents very practical enhancements to the transmission simulator method (TSM); also known as the Modal Constraints for Fixtures and Subsystems (MCFS). The enhancements allow this method to be implemented directly in finite element software, instead of having to extract the reduced finite element model from its software and implement the substructure coupling in another code. The transmission simulator method is useful for coupling substructures where one substructure is derived experimentally and the other is generated from a finite element model. This approach uses a flexible fixture in the experimental substructure to improve the modal basis of the substructure; thus, providing a higher quality substructure. The flexible fixture substructure needs to be removed (decoupled) from the experimental substructure to obtain the true system characteristics. A modified method for this removal and coupling of the experimental and analytical substructures is provided. An additional improvement guarantees that the experimental substructure matrices are positive definite, a requirement for many finite element codes. Guidelines for designing robust transmission simulator hardware are provided. The concepts are applied to two sample cases. The first case consists of a cylinder connected by eight bolts to a plate with a beam. The second example is an outer shell structure that is connected through a bolted flange to a complex internal payload structure. © 2012 Elsevier Ltd. All rights reserved.

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.

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.

Structural dynamic development of modern wind turbines is important for control and to maximize the fatigue life of the wind turbine components. Modeling can be used in development to aid designs. In some cases an experimental dynamic model, or substructure, may be cheaper to develop and more accurate than an analytical model. Some applications for which dynamic substructures could be useful for wind turbine development are presented. 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. Organizations already performing experiments on the test bed are the UK Atomic Weapons Establishment, University of Massachusetts-Lowell, Technical University-Delft and University of Wisconsin. © The Society for Experimental Mechanics, Inc. 2012.

Although analytical substructures have been used successfully for years, practical experimental substructures have been limited to special cases until recently. Many of the historical practical applications were based on a single point attachment. Since substructures have to be connected, theoretically, in both translation and rotation degrees of freedom, measurement translation responses and forces around the single point attachment could be used to estimate the rotational responses and moments. For multiple attachment points, often the rotations and moments have been neglected entirely. In addition, often the effect of the joint stiffness and damping is neglected. The translation simulator approach developed by Allen and Mayes captures the interface forces and motions through a fixture called the transmission simulator, overcoming the historical difficulties. The experimental free modes of the experimental substructure mounted to the transmission simulator and the finite element model of the transmission simulator are used to couple the experimental substructure to another substructure and subtract the transmission simulator. This captures the effects of the joint stiffness and damping. The experimental method and mathematics will be explained with examples. The tutorial assumes a basic understanding of the linear multi-degree of freedom equations of motion and the modal approximation. © 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.