Publications

Abstract not provided.

Abstract not provided.

Abstract not provided.

Multi-shaker vibration testing is gaining interest from structural dynamics test engineers as it can provide a much more accurate match to complicated field vibration responses than traditional single-axis shaker tests. However, the force capabilities of the small modal shakers typically used in multi-shaker vibration tests has limited the achievable response levels. To date, most multi-shaker vibration tests have been performed using a variety of standard, commercially-available control systems. While these control systems are adequate for a wide range of multiple-input/multiple-output tests, their control algorithms have not been tailored for the specific problem of multi-shaker vibration tests: efficiently coordinating the various shakers to work together to achieve a desired response. Here, a new input estimation algorithm is developed and demonstrated using simulations and actual test data. This algorithm, dubbed shape-constrained input estimation, is shown to effectively coordinate multiple shakers using a set of constraint vectors based on the deflection shapes of the test structure. This is accomplished by using the singular vector shapes of the system frequency response matrix, which allows the constraint vectors to automatically change as a function of frequency. Simulation and test results indicate a significant reduction in the input forces required to achieve a desired response. The results indicate that shape-constrained input estimation is an effective method to achieve higher response levels from limited shaker forces which will enable higher level multi-shaker vibration tests to be performed.

Abstract not provided.

Design of multiple-input/multiple-output vibration experiments, such as impedance matched multi-axis testing and multi-shaker testing, rely on a force estimation calculation which is typically executed using a direct inverse approach. Force estimation can be performed multiple ways, each method providing some different tradeoff between response accuracy and input forces. Additionally, there are ways to improve the numerics of the problem with regularization techniques which can reduce errors incurred from poor conditioning of the system frequency response matrix. This paper explores several different force estimation methods and compares several regularization approaches using a simple multiple-input/multiple-output dynamic system, demonstrating the effects on the predicted inputs and responses.

Many in the structural dynamics community are currently researching a range of multiple-input/multiple-output problems and largely rely on commercially-available closed-loop controllers to execute their experiments. Generally, these commercially-available control systems are robust and prove adequate for a wide variety of testing. However, with the development of new techniques in this field, researchers will want to exercise these new techniques in laboratory tests. For example, modifying the control or input estimation method can have benefits to the accuracy of control, or provide higher response for a given input. Modification of the control methods is not typically possible in commercially-available control systems, therefore it is desirable to have some methodology available which allows researchers to synthesize input signals for multiple-input/multiple-output experiments. Here, methods for synthesizing multiply-correlated time histories based on desired cross spectral densities are demonstrated and then explored to understand effects of various parameters on the resulting signals, their statistics, and their relation to the specified cross spectral densities. This paper aims to provide researchers with a simple, step-by-step process which can be implemented to generate input signals for open-loop multiple-input/multiple-output experiments.

The ability to extrapolate response data to unmeasured locations has obvious benefits for a range of lab and field experiments. This is typically done using an expansion process utilizing some type of transformation matrix, which typically comes from mode shapes of a finite element model. While methods exist to perform expansion, it is still not commonplace, perhaps due to a lack of experience using expansion tools or a lack of understanding of the sensitivities of the problem setup on results. To assess the applicability of expansion in a variety of real-world test scenarios, it is necessary to determine the level of perturbation or error the finite element model can sustain while maintaining accuracy in the expanded results. To this end, the structure model’s boundary conditions, joint stiffness, and material properties were altered to determine the range of discrepancies allowable before the expanded results differed significantly from the measurements. The effect of improper implementations of the expansion procedure on accuracy is also explored. This study allows for better insights on prospective use cases and possible pitfalls when implementing the expansion procedure.

Abstract not provided.

Abstract not provided.

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.

Abstract not provided.

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.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.