The purpose of mechanical environment testing is to prove that designs can withstand the loads imparted on them under operating conditions. This is dependent not only on the test article construction but also on the loads imparted through its boundary conditions. Current practices develop environment test specifications from field responses using a single degree of freedom input control with no consideration for the mild to severe deviations from the field motion caused by the laboratory boundary condition. Test specifications are considered conservative with the assumption that most of the steps taken to generate them (e.g., straight-line envelopes and adding 3 dB) result in appropriately conservative specifications. However, without an accurate quantifiable measure of conservatism, designs can be easily mis-tested yielding unnecessarily high costs. Previous work showed a modal model for components excited through base-mounted fixtures to generate specifications with much lower uncertainty and with guaranteed quantifiable conservatism. The method focused on reproducing in-service modal energy in the test configuration by controlling the 6 degree-of-freedom input motion. That work generated test specifications with enough conservatism to account for unit-to-unit variability in the damping of the test article. This paper focuses on generating conservative specifications while considering resonant frequency shifts as a parameter for unit-to-unit variability.
The outline for this presentation includes: Motivation, Test hardware and loads, Modal test of RC on 6 DOF test fixture, and Analysis--develop one specification accounting for unit-to-unit variability and develop independently tailored test specifications for unit-to-unit variability.
The main point of mechanical environment testing is to prove that designs can withstand the loads imparted on them while being exposed to in-service conditions. This is dependent not only on the test article construction, but also the loads imparted through its boundary conditions. Current practices for developing environment test specification are typically based on inadequate information reduced to single input point control with large uncertainty as compared to the field environment. Yet the test specifications are considered conservative, with the assumption that most of the adjustment for uncertainty is conservatism. For base mounted components, a modal model is presented that can be used to generate specifications with much lower uncertainty and with guaranteed quantifiable conservatism. In this method, the modal energies in the fixed base modes of the article due to the in-service loads are determined. Using the fixed base modes of the test article as a basis, the test specification is derived by determining what fixture motion is required to emulate the in-service environment. The specification method accounts for frequency shifts between the in-service and test configurations. Variability in nominal test articles can be included in the derivation of the test specifications. Real hardware under in-service environment loads and in a ground test fixture and loading configuration are considered.
Flight testing provides an opportunity to characterize a system under realistic, combined environments. Unfortunately, the prospect of characterizing flight environments is often accompanied by restrictive instrumentation budgets, thereby limiting the information collected during flight testing. Instrumentation selection is often a result of bargaining to characterize environments at key locations/sub-systems, but may be inadequate to characterize the overall environments or performance of a system. This work seeks to provide an improved method for flight environment characterization through a hybrid experimental-analytical method, modal response extraction, and model expansion. Topics of discussion will include hardware design, assessment of hardware under flight environments, instrumentation planning, and data acquisition challenges. Ground testing and model updating to provide accurate models for expansion will also be presented.
One can estimate unmeasured acceleration spectral density responses of a structure utilizing measured responses from a relatively small number of accelerometers and the active mode shapes provided from a finite element model. The objective in this paper is to demonstrate a similar concept, but purely based on information from a laboratory pre-test. Response predictions can only be calculated at degrees of freedom that have been instrumented in the experimental pre-test, but greater accuracy may be possible than with a finite element-based expansion. A multi-reference set of frequency response functions is gathered in the laboratory pre-test of the field hardware. Two response instrumentation sets are included in the pre-test. One set corresponds to the measurements that will be taken in the field environment. The second set is the field responses that are of great interest but will not be measured in the field environment due to logistical constraints. For example, the second set would provide definition of the component field environment. A set of basis vectors is extracted from the pre-test experimental data in each of multiple frequency bands. Then the field environment is applied to the hardware and the data gathered from the field accelerometers. The basis vectors are then used to expand the response from the field accelerations to the other locations of interest. The proof of concept is provided with an acoustic test environment on the Modal Analysis Test Vehicle. Predicted acceleration spectral density simulations at 14 degrees of freedom (known as “truth responses”) are compared against truth acceleration measurements collected for this work from the acoustic environment. Due to the segregated bandwidth analysis, the required number of field accelerometers to provide the simulation is much smaller than the number of modes in the entire frequency bandwidth.
Many test articles exhibit slight nonlinearities which result in natural frequencies shifting between data from different references. This shifting can confound mode fitting algorithms because a single mode can appear as multiple modes when the data from multiple references are combined in a single data set. For this reason, modal test engineers at Sandia National Laboratories often fit data from each reference separately. However, this creates complexity when selecting a final set of modes, because a given mode may be fit from a number of reference data sets. The color-coded complex mode indicator function was developed as a tool that could be used to reduce a complex data set into a manageable figure that displays the number of modes in a given frequency range and also the reference that best excites the mode. The tool is wrapped in a graphical user interface that allows the test engineer to easily iterate on the selected set of modes, visualize the MAC matrix, quickly resynthesize data to check fits, and export the modes to a report-ready table. This tool has proven valuable, and has been used on very complex modal tests with hundreds of response channels and a handful of reference locations.
Several recent studies (Mayes, R.L., Pacini, B.R., Roettgen, D.R.: A modal model to simulate typical structural dynamics nonlinearity. In: Proceedings of the 34th International Modal Analysis Conference. Orlando, FL, (2016); Pacini, B.R., Mayes, R.L., Owens, B.C., Schultz, R.: Nonlinear finite element model updating, part I: experimental techniques and nonlinear modal model parameter extraction. In: Proceedings of the 35th international modal analysis conference, Garden Grove, CA, (2017)) have investigated predicting nonlinear structural vibration responses using modified modal models. In such models, a nonlinear element is added in parallel to the traditional linear spring and damping elements. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. Previous studies have predominantly applied this method to idealistic structures. In this work, the nonlinear modal modeling technique is applied to a more realistic industrial aerospace structure which exhibits complex bilinear behavior. Linear natural frequencies, damping values, and mode shapes are first extracted from low level shaker testing. Subsequently, the structure is excited using high level tailored shaker inputs. The resulting response data are modally filtered and used to empirically derive the nonlinear elements which, together with their linear counterparts, comprise the nonlinear modal model. This model is then used in both modal and physical domain simulations. Comparisons to measured data are made and the performance of the nonlinear modal model to predict this complex bilinear behavior is discussed.
A previous study in the UK demonstrated that vibration response on a scaled-down model of a missile structure in a wind tunnel could be replicated in a laboratory setting with multiple shakers using an approach dubbed as impedance matching. Here we demonstrate on a full scale industrial structure that the random vibration induced from a laboratory acoustic environment can be nearly replicated at 37 internal accelerometers using six shakers. The voltage input to the shaker amplifiers is calculated using a regularized inverse of the square of the amplitude of the frequency response function matrix and the power spectral density responses of the 37 internal accelerometers. No cross power spectral density responses are utilized. The structure has hundreds of modes and the simulation is performed out to 4000 Hz.
Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.
Experimental dynamic substructuring is a means whereby a mathematical model for a substructure can be obtained experimentally and then coupled to a model for the rest of the assembly to predict the response. Recently, various methods have been proposed that use a transmission simulator to overcome sensitivity to measurement errors and to exercise the interface between the substructures; including the Craig-Bampton, Dual Craig-Bampton, and Craig-Mayes methods. This work compares the advantages and disadvantages of these reduced order modeling strategies for two dynamic substructuring problems. The methods are first used on an analytical beam model to validate the methodologies. Then they are used to obtain an experimental model for structure consisting of a cylinder with several components inside connected to the outside case by foam with uncertain properties. This represents an exceedingly difficult structure to model and so experimental substructuring could be an attractive way to obtain a model of the system.
Experimental dynamic substructuring is a means whereby a mathematical model for a substructure can be obtained experimentally and then coupled to a model for the rest of the assembly to predict the response. Recently, various methods have been proposed that use a transmission simulator to overcome sensitivity to measurement errors and to exercise the interface between the substructures; including the Craig-Bampton, Dual Craig-Bampton, and Craig-Mayes methods. This work compares the advantages and disadvantages of these reduced order modeling strategies for two dynamic substructuring problems. The methods are first used on an analytical beam model to validate the methodologies. Then they are used to obtain an experimental model for structure consisting of a cylinder with several components inside connected to the outside case by foam with uncertain properties. This represents an exceedingly difficult structure to model and so experimental substructuring could be an attractive way to obtain a model of the system.
Qualification of complex systems typically involves testing the components individually in shock and vibration environments before assembling them into the system. When the components are secured to a fixture on the shaker table, the mechanical impedance of the boundary condition is quite different from that of the next level of assembly. Thus the modes of the component under test are not excited in the same way that they are excited in the system using the typical methods for defining input specifications. Here, the boundary condition impedance is investigated and quantified using substructuring techniques. Also, fixture inputs are derived to overcome the impedance differences and excite a component in the same way it is excited in the next level of assembly.
Conference Proceedings of the Society for Experimental Mechanics Series
Allen, Matthew S.; Roettgen, Daniel; Kammer, Daniel; Mayes, R.L.
This work proposes a means whereby weak nonlinearity in a substructure, as typically arises due to friction in bolted interfaces, can be captured experimentally on a mode-by-mode basis and then used to predict the nonlinear response of an assembly. The method relies on the fact that the modes of a weakly nonlinear structure tend to remain uncoupled so long as their natural frequencies are distinct and higher harmonics generated by the nonlinearity do not produce significant response in other modes. Recent experiments on industrial hardware with bolted joints has shown that this type of model can be quite effective, and that a single degree-of-freedom (DOF) system with an Iwan joint, which is known as a modal Iwan model, effectively captures the way in which the stiffness and damping depend on amplitude. Once the modal Iwan models have been identified for each mode of the subcomponent(s) of interest, they can be assembled using standard techniques and used with a numerical integration routine to compute the nonlinear transient response of the assembled structure. The proposed methods are demonstrated by coupling a modal model of a 3DOF system with three discrete Iwan joints to a linear model for a 2DOF system.
Experimental-analytical substructuring is attractive when there is motivation to replace one or more system subcomponents with an experimental model. This experimentally derived substructure can then be coupled to finite element models of the rest of the structure to predict the system response. The transmission simulator method couples a fixture to the component of interest during a vibration test in order to improve the experimental model for the component. The transmission simulator is then subtracted from the tested system to produce the experimental component. The method reduces ill-conditioning by imposing a least squares fit of constraints between substructure modal coordinates to connect substructures, instead of directly connecting physical interface degrees of freedom. This paper presents an alternative means of deriving the experimental substructure model, in which a Craig-Bampton representation of the transmission simulator is created and subtracted from the experimental measurements. The corresponding modal basis of the transmission simulator is described by the fixed-interface modes, rather than free modes that were used in the original approach. These modes do a better job of representing the shape of the transmission simulator as it responds within the experimental system, leading to more accurate results using fewer modes. The new approach is demonstrated using a simple finite element model based example with a redundant interface.
Experiments were performed to understand the complex fluid-structure interactions that occur during aircraft internal store carriage. A cylindrical store was installed in a rectangular cavity having a length-to-depth ratio of 3.33 and a length-to-width ratio of 1. The Mach number ranged from 0.6 to 2.5 and the incoming boundary layer was turbulent. Fast-response pressure measurements provided aeroacoustic loading in the cavity, while triaxial accelerometers provided simultaneous store response. Despite occupying only 6% of the cavity volume, the store significantly altered the cavity acoustics. The store responded to the cavity flow at its natural structural frequencies, and it exhibited a directionally dependent response to cavity resonance. Specifically, cavity tones excited the store in the streamwise and wall-normal directions consistently, whereas a spanwise response was observed only occasionally. The streamwise and wall-normal responses were attributed to the longitudinal pressure waves and shear layer vortices known to occur during cavity resonance. Although the spanwise response to cavity tones was limited, broadband pressure fluctuations resulted in significant spanwise accelerations at store natural frequencies. The largest vibrations occurred when a cavity tone matched a structural natural frequency, although energy was transferred more efficiently to natural frequencies having predominantly streamwise and wall-normal motions.
A collaborative research institute was organized and held at Sandia Albuquerque for a period of six weeks. This research institute brought together researchers from around the world to work collaboratively on a set of research projects. These research projects included: developing experimental guidelines for studying variability and repeatability of nonlinear structures; decoupling aleatoric and epistemic uncertainty in measurements to improve dynamic predictions; a numerical round robin to assess the performance of five different numerical codes for modeling systems with strong nonlinearities; and an assessment of experimentally derived and numerically derived reduced order models. In addition to the technical collaborations, the institute also included a series of seminars given by both Sandians and external experts, as well as a series of tours and field trips to local places of scientific and engineering importance. This report details both the technical research and the programmatic organization of the 2014 Sandia Nonlinear Mechanics and Dynamics Summer Research Institute.
This work was motivated by a desire to transform an experimental dynamic substructure derived using the transmission simulator method into the Craig-Bampton substructure form which could easily be coupled with a finite element code with the Craig-Bampton option. Near the middle of that derivation, a modal Craig-Bampton form emerges. The modal Craig-Bampton (MCB) form was found to have several useful properties. The MCB matrices separate the response into convenient partitions related to (1) the fixed boundary modes of the substructure (a diagonal partition), (2) the modes of the fixture it is mounted upon, (3) the coupling terms between the two sets of modes. Advantages of the MCB are addressed. (1) The impedance of the boundary condition for component testing, which is usually unknown, is quantified with simple terms. (2) The model is useful for shaker control in both single degree of freedom and multiple degree of freedom shaker control systems. (3) MCB provides an energy based framework for component specifications to reduce over-testing but still guarantee conservatism.
Experimental dynamic substructures in both modal and frequency response domains using the transmission simulator method have been developed for several systems since 2007. The standard methodology couples the stiffness, mass and damping matrices of the experimental substructure to a finite element (FE) model of the remainder of the system through multi-point constraints. This can be somewhat awkward in the FE code. It is desirable to have an experimental substructure in the Craig-Bampton (CB) form to ease the implementation process, since many codes such as Nastran, ABAQUS, ANSYS and Sierra Structural Dynamics have CB as a substructure option. Many analysts are familiar with the CB form. A square transformation matrix is derived that produces a modified CB form that still requires multi-point constraints to couple to the rest of the FE model. Finally the multi-point constraints are imported to the modified CB matrices to produce substructure matrices that fit in the standard CB form. The physical boundary degrees-of-freedom (dof) of the experimental substructure matrices can be directly attached to physical dof in the remainder of the FE model. This paper derives the new experimental substructure that fits in the CB form, and presents results from an analytical and an industrial example utilizing the new CB form.
This paper contains an example of the transmission simulator method for experimental dynamic substructuring using the Ampair 600Wind Turbine. The structure of interest is the hub-and-three-bladed assembly. A single blade and hub is used as a substructure to develop a model for the hub-and-three-bladed assembly. The single-blade-and-hub substructure was developed from elastic modes of a free-free test and rigid body modes analytically derived from measured mass properties. This substructure can be rotated and replicated using the hub as a transmission simulator. Substructuring calculations were then performed using the transmission simulator method to derive a model of the hub-and-three-bladed assembly. This paper concludes with a comparison for this combined model to truth data derived from a free-free modal test of the entire rotor.
Developing constitutive models of the physics in mechanical joints is currently stymied by inability to measure forces and displacements within the joint. The current state of the art estimates whole joint stiffness and energy loss per cycle from external measured force input and one or two acceleration responses. To validate constitutive models beyond this state requires a measurement of the distributed forces and displacements at the joint interface. Unfortunately, introducing measurement devices at the interface completely disrupts the desired physics. A feasibility study is presented for a non-intrusive method of solving for the interface dynamic forces from an inverse problem using full field measured responses. The responses come from the viewable surface of a beam. The noise levels associated with digital image correlation and continuous scanning laser Doppler velocimetry are evaluated from typical beam experiments. Two inverse problems are simulated. One utilizes the extended Sum of Weighted Accelerations Technique (SWAT). The second is a new approach dubbed the method of truncated orthogonal forces. These methods are much more robust if the contact patch geometry is well identified. Various approaches to identifying the contact patch are investigated, including ion marker tracking, Prussian blue and ultrasonic measurements. A typical experiment is conceived for a beam which has a lap joint at one end with a single bolt connecting it to another identical beam. In a virtual test using the beam finite element analysis, it appears that the SWAT inverse method requires evaluation of too many coefficients to adequately identify the force distribution to be viable. However, the method of truncated orthogonal forces appears viable with current digital image correlation (and probably other) imaging techniques.
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.