Publications

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Laser vibrometry has become a mature technology for structural dynamics testing, enabling many measurements to be obtained in a short amount of time without mass-loading the part. Recently multi-point laser vibrometers consisting of 48 or more measurement channels have been introduced to overcome some of the limitations of scanning systems, namely the inability to measure multiple data points simultaneously. However, measuring or estimating the alignment (Euler angles) of many laser beams for a given test setup remains tedious and can require a significant amount of time to complete and adds an unquantified source of uncertainty to the measurement. This paper introduces an alignment technique for the multipoint vibrometer system that utilizes photogrammetry to triangulate laser spots from which the Euler angles of each laser head relative to the test coordinate system can be determined. The generated laser beam vectors can be used to automatically create a test geometry and channel table. While the approach described was performed manually for proof of concept, it could be automated using the scripting tools within the vibrometer system.

The Box Assembly with Removable Component (BARC) structure was developed as a challenge problem for those investigating boundary conditions and their effect on structural dynamic tests. To investigate the effects of boundary conditions on the dynamic response of the Removable Component, it was tested in three configurations, each with a different fixture and thus a different boundary condition. A “truth” configuration test with the component attached to its next-level assembly (the Box) was first performed to provide data that multi-axis tests of the component would aim to replicate. The following two tests aimed to reproduce the component responses of the first test through multi-axis testing. The first of these tests is a more “traditional” vibration test with the removable component attached to a “rigid” plate fixture. A second set of these tests replaces the fixture plate with flexible fixtures designed using topology optimization and created using additive manufacturing. These two test approaches are compared back to the truth test to determine how much improvement can be obtained in a laboratory test by using a fixture that is more representative of the compliance of the component’s assembly.

Multi-axis testing is growing in popularity in the testing community due to its ability to better match a complex three-dimensional excitation than a single-axis shaker test. However, with the ability to put a large number of shakers anywhere on the structure, the design space of such a test is enormous. This paper aims to investigate strategies for placement of shakers for a given test using a complex aerospace structure controlled to real environment data. Initially shakers are placed using engineering judgement, and this was found to perform reasonably well. To find shaker setups that improved upon engineering judgement, impact testing was performed at a large number of candidate excitation locations to generate frequency response functions that could be used to perform virtual control studies. In this way, a large number of shaker positions could be evaluated without needing to reposition the shakers each time. A brute force computation of all possible shaker setups was performed to find the set with the lowest error, but the computational cost of this approach is prohibitive for very large candidate shaker sets. Instead, an iterative approach was derived that found a suboptimal set that was nearly as good as the brute force calculation. Finally, an investigation into the number of shakers used for control was performed, which could help determine how many shakers might be necessary to perform a given test.

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Understanding the dynamic response of a structure is critical to design. This is of extreme importance in high-consequence systems on which human life can depend. Historically, these structures have been modeled as linear, where response scales proportionally with excitation amplitude. However, most structures are nonlinear to the extent that linear models are no longer sufficient to adequately capture important dynamics. Sources of nonlinearity include, but are not limited to: large deflections (so called geometric nonlinearities), complex materials, and frictional interfaces/joints in assemblies between subcomponents. Joint nonlinearities usually cause the natural frequency to decrease and the effective damping ratio to increase with response amplitude due to microslip effects. These characteristics can drastically alter the dynamics of a structure and, if not well understood, could lead to unforeseen failure or unnecessarily over-designed features. Nonlinear structural dynamics has been a subject of study for many years, and provide a summary of recent developments and discoveries in this field. One topic discussed in these papers are nonlinear normal modes (NNMs) which are periodic solutions of the underlying conservative system. They provide a theoretical framework for describing the energy-dependence of natural frequencies and mode shapes of nonlinear systems, and lead to a promising method to validate nonlinear models. In and, a force appropriation testing technique was developed which allowed for the experimental tracking of undamped NNMs by achieving phase quadrature between the excitation and response. These studies considered damping to be small to moderate, and constant. Nonlinear damping of an NNM was studied in using power-based quantities for a structure with a discrete, single-bolt interface. In this work, the force appropriation technique where phase quadrature is achieved between force and response as described in is applied to a target mode of a structure with two bolted joints, one of which comprised a large, continuous interface. This is a preliminary investigation which includes a study of nonlinear natural frequency, mode shape, and damping trends extracted from the measured data.

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Experiments, modeling and simulation were used to study the nonlinear dynamics of a jointed-structure in a shock tube. The structure was a full-span square cylinder with internal bolted connections excited by fluid loading. The width-based Reynolds number was ≈10⁵. The cylinder was exposed to an impulsive force associated with the incident shock followed by transverse loading imposed by vortex shedding. In the experiment, aerodynamic loading was characterized with high-speed pressure sensitive paint (PSP). Digital image correlation (DIC) concurrently measured the structural response. The maximum displacement occurred when the vortex shedding frequency most closely matched the structural mode of the beam associated with a rocking motion at the joint. A finite element model was developed using Abaqus, where the nonlinear contact dynamics of the joint were simulated using Coulomb friction. The PSP data loaded the model and the interaction was treated as one-way coupled. The simulations well-matched the trends observed in the experiment. Overall, the root-mean-square values of the transverse displacement agreed to within 24% of the experiment. The modeling showed rocking about the joint during vortex shedding was critical to the nonlinear damping and energy dissipation in the structure. We conclude this campaign highlights the importance of jointed-connections to energy dissipation in structures under aerodynamic loading.

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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.

Small components are becoming increasingly prevalent in today’s society. Springs are a commonly found piece-part in many mechanisms, and as these components become smaller, so do the springs inside of them. Because of their size, small manufacturing defects or other damage to the spring may become significant: a tiny gouge might end up being a significant portion of the cross-sectional area of the wire. However, their small size also makes it difficult to detect such flaws and defects in an efficient manner. This work aims to investigate the effectiveness of using dynamic measurements to detect damage to a miniature spring. Due to their small size, traditional instrumentation cannot be used to take measurements on the spring. Instead, the non-contact Laser Doppler Vibrometry technique is investigated. Natural frequencies and operating shapes are measured for a number of springs. These results are compared against springs that have been intentionally flawed to determine if the change in dynamic properties is a reasonable metric for damage detection.

Many methods have been proposed for updating finite element matrices using experimentally derived modal parameters. By using these methods, a finite element model can be made to exactly match the experiment. These techniques have not achieved widespread use in finite element modeling because they introduce non-physical matrices. Recently, Scanning Laser Doppler Vibrometery (SLDV) has enabled finer measurement point resolution and more accurate measurement point placement with no mass loading compared to traditional accelerometer or roving hammer tests. Therefore, it is worth reinvestigating these updating procedures with high-resolution data inputs to determine if they are able to produce finite element models that are suitable for substructuring. A rough finite element model of an Ampair Wind Turbine Blade was created, and a SLDV measurement was performed that measured three-dimensional data at every node on one surface of the blade. This data was used to update the finite element model so that it exactly matched test data. A simple substructuring example of fixing the base of the blade was performed and compared to previously measured fixed-base data.

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