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.
This paper investigates methods for coupling analytical dynamic models of subcomponents with experimentally derived models in order to predict the response of the combined system, focusing on modal substructuring or Component Mode Synthesis (CMS), the experimental analog to the ubiquitous Craig-Bampton method. While the basic methods for combining experimental and analytical models have been around for many years, it appears that these are not often applied successfully. The CMS theory is presented along with a new strategy, dubbed the Maximum Rank Coordinate Choice (MRCC), that ensures that the constrained degrees of freedom can be found from the unconstrained without encountering numerical ill conditioning. The experimental modal substructuring approach is also compared with frequency response function coupling, sometimes called admittance or impedance coupling. These methods are used both to analytically remove models of a test fixture (required to include rotational degrees of freedom) and to predict the response of the coupled beams. Both rigid and elastic models for the fixture are considered. Similar results are obtained using either method although the modal substructuring method yields a more compact database and allows one to more easily interrogate the resulting system model to assure that physically meaningful results have been obtained. A method for coupling the fixture model to experimental measurements, dubbed the Modal Constraint for Fixture and Subsystem (MCFS) is presented that greatly improves the result and robustness when an elastic fixture model is used.
Techniques to ensure shock data quality and to recognize bad data are discussed in this paper. For certain shock environments, acceleration response up to ten kHz is desired for structural model validation purposes. The validity and uncertainty associated with the experimental data need to be known in order to use it effectively in model validation. In some cases the frequency content of impulsive or pyrotechnic loading or metal to metal contact of joints in the structure may excite accelerometer resonances at hundreds of kHz. The piezoresistive accelerometers often used to measure such events can provide unreliable data depending on the level and frequency content of the shock. The filtered acceleration time history may not reveal that the data are unreliable. Some data validity considerations include accelerometer mounting systems, sampling rates, band-edge settings, peak acceleration specifications, signal conditioning bandwidth, accelerometer mounted resonance and signal processing checks. One approach for uncertainty quantification of the sensors, signal conditioning and data acquisition system is also explained.
Multiple references are often used to excite a structure in modal testing programs. This is necessary to excite all the modes and to extract accurate mode shapes when closely spaced roots are present. An algorithm known as SMAC (Synthesize Modes And Correlate), based on principles of modal filtering, has been in development for several years. This extraction technique calculates reciprocal modal vectors based on frequency response function (FRF) measurements. SMAC was developed to accurately extract modes from structures with moderately damped modes and/or high modal density. In the past SMAC has only worked with single reference data. This paper presents an extension of SMAC to work with multiple reference data. If roots are truly perfectly repeated, the mode shapes extracted by any method will be a linear combination of the "true" shapes. However, most closely spaced roots are not perfectly repeated but have some small difference in frequency and/or damping. SMAC exploits these very small differences. The multi-reference capability of SMAC begins with an evaluation of the MMIF (Multivariate Mode Indicator Function) or CMIF (Complex Mode Indicator Function) from the starting frequency list to determine which roots are likely repeated. Several seed roots are scattered in the region of the suspected multiple roots and convergence is obtained. Mode shapes are then created from each of the references individually. The final set of mode shapes are selected based on one of three different selection techniques. Each of these is presented in this paper. SMAC has long included synthesis of FRFs and MIFs from the roots and residues to check extraction quality against the original data, but the capability to include residual effects has been minimal. Its capabilities for including residual vectors to account for out-of-band modes have now been greatly enhanced. The ability to resynthesize FRFs and mode indicator functions from the final mode shapes and residual information has also been developed. Examples are provided utilizing the SMAC package on multi-reference experimental data from two different systems.
A finite element (FE) model of a shell-payload structure is to be used to predict structural dynamic acceleration response to untestable blast environments. To understand the confidence level of these predictions, the model will be validated using test data from a blast tube experiment. The first step in validating the structural response is to validate the loading. A computational fluid dynamics (CFD) code, Saccara, was used to provide the blast tube pressure loading to the FE model. This paper describes the validation of the CFD pressure loading and its uncertainty quantification with respect to experimental pressure data obtained from geometrical mock-up structures instrumented with pressure gages in multiple nominal blast tube tests. A systematic validation approach was used from the uncertainty quantification group at Sandia National Labs. Significant effort was applied to distill the pressure loading to a small number of validation metrics important to obtaining valid final response which is in terms of acceleration shock response spectrum. Uncertainty in the pressure loading amplitude is quantified so that it can be applied to the validation blast tube test on the shell payload structure which has significant acceleration instrumentation but only a few pressure gages.
In modal testing, the most popular tools for exciting a structure are hammers and shakers. This paper reviews the applications for which shakers have an advantage. In addition the advantages and disadvantages of different forcing inputs (e.g. sinusoidal, random, burst random and chirp) that can be applied with a shaker are noted. Special considerations are reported for the fixtures required for shaker testing (blocks, force gages, stingers) to obtain satisfactory results. Various problems that the author has encountered during single and multi-shaker modal tests are described with their solutions.
The purpose of modal testing is usually to provide an estimate of a linear structural dynamics model. Typical uses of the experimental modal model are (1) to compare it with a finite element model for model validation or updating; (2) to verify a plant model for a control system; or (3) to develop an experimentally based model to understand structural dynamic responses. Since these are some common end uses, for this article the main goal is to focus on excitation methods to obtain an adequate estimate of a linear structural dynamics model. The purpose of the modal test should also provide the requirements that will drive the rigor of the testing, analysis, and the amount of instrumentation. Sometimes, only the natural frequencies are required. The next level is to obtain relative mode shapes with the frequencies to correlate with a finite element model. More rigor is required to get accurate critical damping ratios if energy dissipation is important. At the highest level, a full experimental model may require the natural frequencies, damping, modal mass, scaled shapes, and, perhaps, other terms to account for out-of-band modes. There is usually a requirement on the uncertainty of the modal parameters, whether it is specifically called out or underlying. These requirements drive the meaning of the word 'adequate' in the phrase 'adequate linear estimate' for the structural dynamics model. The most popular tools for exciting structures in modal tests are shakers and impact hammers. The emphasis here will be on shakers. There have been many papers over the years that mention some of the advantages and issues associated with shaker testing. One study that is focused on getting good data with shakers is that of Peterson. Although impact hammers may seem very convenient, in many cases, shakers offer advantages in obtaining a linear model. The best choice of excitation device is somewhat dependent on the test article and logistical considerations. These considerations will be addressed in this article to help the test team make a choice between impact hammer and various shaker options. After the choice is made, there are still challenges to obtaining data for an adequate linear estimate of the desired structural dynamics model. The structural dynamics model may be a modal model with the desired quantities of natural frequencies, viscous damping ratios, and mode shapes with modal masses, or it may be the frequency response functions (FRFs), or their transforms, which may be constructed from the modal model. In any case, the fidelity of the linear model depends to a large extent on the validity of the experimental data, which are generally gathered in the form of FRFs. With the goal of obtaining an 'adequate linear estimate' for a model of the structural dynamic system under test, consider several common challenges that must be overcome in the excitation setup to gather adequate data.
In linear finite element models, proportional damping is often used. In general this does not produce results that match experimental measurements. Modal damping is a much better option, but sometimes is incovenient. It may be cumbersome to calculate all the modes and keep track of what damping should be applied to each mode. If an explicit code is used, the modes are not available directly, so modal damping cannot be applied. A new approximate algorithm is demonstrated which allows the damping to be applied to undamped model response time histories. The damping is applied in user chosen frequency bands to as high a frequency as desired. Different damping may be applied to each response location. The method is demonstrated to be virtually equivalent to applying modal damping in bands. Examples are shown for a two degree of freedom spring-mass-damper system and a finite element model with 100 modes in the bandwidth.
Experienced experimentalists have gone through the process of attempting to identify a final set of modal parameters from several different sets of extracted parameters. Usually, this is done by visually examining the mode shapes. With the advent of automated modal parameter extraction algorithms such as SMAC (Synthesize Modes and Correlate), very accurate extractions can be made to high frequencies. However, this process may generate several hundred modes that then must be consolidated into a final set of modal information. This as motivated the authors to generate a set of tools to speed the process of consolidating modal parameters by mathematical (instead of visual) means. These tools help quickly identify the best modal parameter extraction associated with several extractions of the same mode. The tools also indicate how many different modes have been extracted in a nominal frequency range and from which references. The mathematics are presented to achieve the best modal extraction of multiple modes at the same nominal frequency. Improvements in the SMAC graphical user interface and database are discussed that speed and improve the entire extraction process.