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Thomas G. Came, Randy L. Mayas and Vesta I. Bateman .... _ i_ _ :!_ Sandia NationalLaboratories _. .... Albuquerque, NewMexico87185, USA ' _ i_ _ / ABSTRACT important design consideration. This would include payloador satelliteloads duringrocket launches[3]. Force reconstruction is a procedure in which the externally applied force is inferred from measured An applicationthat will be discussed as part of this structuralresponse ratherthan directlymeasured. In paper is the impact into a rigid barrier of a weapon a recently developed technique, the response system with an energy-absorbing nose. The nose acceleration time-histories are multiplied by scalar had been designed to absorb the energy of impact weights and summed to produce the reconstructed and to mitigate the shock to the interiorcomponents. force. This reconstruction is called the Sum of To evaluate the crush capabilityof the nose, impact Weighted Accelerations Technique (SWAT). One tests were performed, and the measured forcestep in the application of this technique is the displacement curve was compared to the design calculationof the appropriatescalar weights. In this objective. Figure 1 shows the weapon mass-mockup paper a new methodof estimatingthe weights, using with the energy absorbing nose hung from its launch measured frequency response function data, is rail and fixture. The mass-mockup was designed to developed and contrasted with the traditional SWAT have the same mass, center-of-mass, and momentmethod of inverting the mode-shape matrix. The of-inertia as the real weapon. Both axial and diagonal techniqueuses frequency responsefunctiondata, but impact tests of the nose were plannedso the mockis not based on deconvolution, up needed to possess the correct rigid-bodyinertiaas well as mass. Figure2 showsthe plasticdeformation This work was supported by the U. S. Department of '_ _,. Energy under contract No. DE-AC04-94AL85000. _,t _ ]L. __ c_ .Olr. _P_[J'i ;_; '} :" "H]_; D0/CUt_.Ft'4T J:_i.JIYLI,_ITF._ DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer er, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Epistemic uncertainty, characterizing lack-of-knowledge, is often prevalent in engineering applications. However, the methods we have for analyzing and propagating epistemic uncertainty are not as nearly widely used or well-understood as methods to propagate aleatory uncertainty (e.g. inherent variability characterized by probability distributions). In this paper, we examine three methods used in propagating epistemic uncertainties: interval analysis, Dempster-Shafer evidence theory, and second-order probability. We demonstrate examples of their use on a problem in structural dynamics, specifically in the assessment of margins. In terms of new approaches, we examine the use of surrogate methods in epistemic analysis, both surrogate-based optimization in interval analysis and use of polynomial chaos expansions to provide upper and lower bounding approximations. Although there are pitfalls associated with surrogates, they can be powerful and efficient in the quantification of epistemic uncertainty.

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Correlation of test and analysis mode shapes using reduced Test Analysis Models (TAMs) has become an industry standard method used to validate finite element models. Some organizations have even mandated specific metrics regarding the allowable deviations in the orthogonality of mode shapes, using the TAM mass matrix, that a model must meet to be considered valid. As a result, significant effort has been directed towards developing robust TAMs and in comparing the robustness of the various approaches. The static or Guyan reduction method has been touted as the most robust, although the evidence in the literature seems quite inconclusive. This work takes a new view on test analysis orthogonality, utilizing a probabilistic framework to accurately quantify the sensitivity of the Static, Modal and IRS reduction methods to errors in a set of mode shapes for a general satellite FEA model. The results show that the orthogonality calculation is highly sensitive to errors, so that the Static and IRS TAM models have a very small probability of passing the orthogonality criteria, when the true mode shapes are used, contaminated by only a small level of noise. This study also shows that the performance of the Modal TAM depends heavily on the sensor set chosen; the sensitivity of the modal TAM was observed to increase fourfold when a Static TAM sensor set was used rather than one that was optimized specifically for the Modal TAM. The results are also evaluated in light of one theory that relates sensitivity to the natural frequencies of the system constrained at the sensor locations, revealing that the theory fails for the Modal TAM yet may perhaps hold for the IRS TAM. While a conclusive ranking of the TAM methods cannot be achieved using a single model, this work presents the tools, based on a probabilistic framework, that can be used to correctly ascertain the sensitivity of test analysis models and to evaluate to model validation methodology. 1 Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U.S. Department of Energy under Contract DE-AC04-94AL85000. FEM, called a test-analysis model (TAM) must be generated. The orthogonality of the modes can then be computed with respect to the reduced analytical mass matrix, or TAM mass matrix [1]. The use of these metrics, and the required values for test/analysis correlation, are dictated by agencies such as NASA [2] and the United States Air Force [1]. Depending on the agency, the requirements are different. For example, the Air Force requires test/analysis frequency errors less than or equal to 3.0%, cross-generalized mass values greater than 0.95, and coupling terms between modes of less than 0.10 in test-orthogonality and test-FEM cross-orthogonality.

An algorithm originally used to locate errors in finite element models is applied to a fuil scale bridge damage detection experiment. The method requires experimental frequency response function data measured at discrete locations along the major bridge load paths. In the bridge damage application the algorithm is most effective when applied to static flexibility shapes estimated with a truncated set of six mode shapes rather than individual mode shapes. The algorithm compares "before damage" and "after damage" data to locate physical areas where significant stiffness changes have occurred. A damage indicator shows whether damage is detectable. Damage is correctly located in the two most significant damage cases using the driving point static flexibility estimates. Limitations of the technique are addressed. The damage detection experiment was performed on a three span steel girder bridge that was 425 feet long.

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.