Publications

In recent years, a successful method for generating experimental dynamic substructures has been developed using an instrumented fixture, the transmission simulator. The transmission simulator method solves many of the problems associated with experimental substructuring. These solutions effectively address: 1. rotation and moment estimation at connection points; 2. providing substructure Ritz vectors that adequately span the connection motion space; and 3. adequately addressing multiple and continuous attachment locations. However, the transmission simulator method may fail if the transmission simulator is poorly designed. Four areas of the design addressed here are: 1. designating response sensor locations; 2. designating force input locations; 3. physical design of the transmission simulator; and 4. modal test design. In addition to the transmission simulator design investigations, a review of the theory with an example problem is presented.

Estimation of the uncertainty in experimental modal parameters is valuable when validation of a finite element model is performed based on modal frequencies and shapes. The uncertainty in the data is needed to establish distribution functions for the comparison to computational models. A part that is typically neglected with the experimental data is to quantify the uncertainty in the estimated parameters established from the data. This uncertainty is an important piece of the puzzle in a validation exercise. If the uncertainty in the fit is not accounted for, the uncertainty estimate of the experimental data is incomplete. This paper will explore the uncertainty of the modal parameter estimates measured from the Synthesize Modes and Correlate (SMAC) algorithm using a Monte Carlo technique. The uncertainty in the parameter fit will be determined for both analytically and experimentally determined frequency response functions. It is found that the largest uncertainty in the SMAC algorithm is within the optimization step of the fitting process. © 2009 Society for Experimental Mechanics Inc.

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.

Analytic model validation assesses the usefulness of a model for its intended purpose. Validation of the model should be based on a blind prediction of test results, so that the predictive capability is demonstrated. However, there is certainly a place in the validation process for exercising the model in correlation and calibration before making the final blind validation prediction. In many cases, the initial model deviates from a useful state for unknown or unquantified reasons. Then model correlation exercises are performed. The term "correlation" for structural dynamics comes from the initial one to one correlation of the modes of the model with modes from a modal test. But correlation really includes more than just this initial comparison. Correlation exercises can uncover unintended errors or incorrect assumptions and simplifications in the thousands of details important to model development. Calibration, on the other hand, is designed to improve estimates on specific uncertain parameters. Sensitivity analysis is examined as a method for calibration. Sensitivity analysis is an inferential process that has definite limits, and three tools for understanding those limits are provided. In some cases, calibration does not provide sufficient model improvement, and additional correlation exercises are performed after the calibration. Often correlation and calibration are most effective when applied to subsystems of the model to isolate specific errors. © 2009 Society for Experimental Mechanics Inc.

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.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

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.

Abstract not provided.

Abstract not provided.

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.

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.

Abstract not provided.

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.

Abstract not provided.

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 has 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.

An algorithm known as SMAC (Synthesize Modes And Correlate), based on principles of modal filtering, has been in development for a few years. The new capabilities of the automated version are demonstrated on test data from a complex shell/payload system. Examples of extractions from impact and shaker data are shown. The automated algorithm extracts 30 to 50 modes in the bandwidth from each column of the frequency response function matrix. Examples of the synthesized Mode Indicator Functions (MIFs) compared with the actual MIFs show the accuracy of the technique. A data set for one input and 170 accelerometer outputs can typically be reduced in an hour. Application to a test with some complex modes is also demonstrated.

As model validation techniques gain more acceptance and increase in power, the demands on the modal parameter extractions increase. The estimation accuracy, the number of modes desired, and the data reduction efficiency are required features. An algorithm known as SMAC (Synthesize Modes And Correlate), based on principles of modal filtering, has been in development for a few years. SMAC has now been extended in two main areas. First, it has now been automated. Second, it has been extended to fit complex modes as well as real modes. These extensions have enhanced the power of modal extraction so that, typically, the analyst needs to manually fit only 10 percent of the modes in the desired bandwidth, whereas the automated routines will fit 90 percent of the modes. SMAC could be successfully automated because it generally does not produce computational roots.

A popular method for updating finite element models with modal test data utilizes optimization of the model based on design sensitivities. The attractive feature of this technique is that it allows some estimate and update of the physical parameters affecting the hardware dynamics. Two difficulties are knowing which physical parameters are important and which of those important parameters are in error. If this is known, the updating process is simply running through the mechanics of the optimization. Most models of real systems have a myriad of parameters. This paper discusses an implementation of a tool which uses the model and test data together to discover which parameters are most important and most in error. Some insight about the validity of the model form may also be obtained. Experience gained from applications to complex models will be shared.

New Mexico State University organized an effort to perform static and dynamic damage-detection tests on the Interstate-40 bridge over the Rio Grande at Albuquerque. The opportunity was available because the 425-ft-long bridge was soon to be replaced. Sandia National Laboratories was asked to provide and operate a shaker that could exert 1000-lb peak amplitude forces for both sinusoidal and random excitations between 2 and 20 Hz. Two Sandia departments collaborated to design and build the shaker, using existing major components connected with Sandia-designed and -fabricated hardware. The shaker was installed and operated successfully for a series of five modal and sinusoidal response tests.