Publications

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The goal of this work is to build model credibility of a structural dynamics model by comparing simulated responses to measured responses in random vibration environments, with limited knowledge of the true test input. Oftentimes off-axis excitations can be introduced during single axis vibration testing in the laboratory due to shaker or test fixture dynamics and interface variation. Model credibility cannot be improved by comparing predicted responses to measured responses with unknown excitation profiles. In the absence of sufficient time domain response measurements, the true multi-degree-of-freedom input cannot be exactly characterized for a fair comparison between the model and experiment. Methods exist, however, to estimate multi-degree-of-freedom (MDOF) inputs required to replicate field test data in the laboratory Ross et al.: 6-DOF Shaker Test Input Derivation from Field Test. In: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics, Bethel (2017). This work focuses on utilizing one of these methods to approximately characterize the off-axis excitation present during laboratory random vibration testing. The method selects a sub-set of the experimental output spectral density matrix, in combination with the system transmissibility matrix, to estimate the input spectral density matrix required to drive the selected measurement responses. Using the estimated multi-degree-of-freedom input generated from this method, the error between simulated predictions and measured responses was significantly reduced across the frequency range of interest, compared to the error computed between experimental data to simulated responses generated assuming single axis excitation.

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Component mode synthesis (CMS) is a widely employed model reduction technique used to reduce the computational cost associated with the dynamic analysis of complex engineering structures. To generate CMS models, specifically the formulation of Craig and Bampton, both normal fixed-interface modes and constraint modes of the component’s structure are calculated. These modes are used in conjunction with the component level mass and stiffness matrices to generate reduced mass and stiffness matrices used in the final analyses. For some component models, the most computationally expensive part of this procedure is calculating the component normal modes information. Several different approaches are utilized to investigate the sensitivity of system level responses to variations in several aspects of the CMS models. One approach evaluates changes due to modifications of the reduced mass and stiffness matrices assuming that the mode shapes do not change. The second approach assumes that the mode shapes change but the reduced mass and stiffness matrices do not change. An example is presented to show the influence of these two approaches.

We propose the use of the Primary Complex Mode Indicator Function (PCMIF), calculated from acceleration frequency response functions, as a response comparison metric to analyze unit-to-unit variability. The PCMIF has an advantage over the traditional dynamic representations of mode shapes, frequencies and damping in that it removes the user and algorithmic error that may be associated with those extractions. In addition, it is customizable according to the interest level. If consistent sets of acceleration measurements from chosen drive points can be acquired from multiple hardware units, the comparison of each unit's PCMIF metric can provide insight. In addition to measured PCMIF, finite element models of the system can predict variability in PCMIF response using known variability of hardware configurations, and this can be compared with experimental PCMIF data. This comparison allows meaningful unit-to-unit comparison even if components and/or system geometries differ from one system to the next.