Date of Award:

5-2016

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mechanical and Aerospace Engineering

Committee Chair(s)

Steven Folkman

Committee

Steven Folkman

Committee

Thomas Fronk

Committee

David Geller

Committee

Marvin Halling

Committee

Benjamin Goldberg

Abstract

Component requirements govern design and production in the aerospace industry. One such potential requirement for a component is the survival and continued function upon exposure to shock environments. A shock event is a high amplitude, short duration traveling wave that induces large loads on components in its path that can cause degradation of electronic components, cracks and fractures in brittle materials, local plastic deformation, and materials to experience accelerated fatigue life. In defining these environments for new structures, industry experts rely mainly on empirical data. Measurements from similar structures are scaled and enveloped to create a predicted bounding case. This enveloping process is often times conservative which leads to increased design and risk reduction costs. This work focuses on two ways to aid in the reduction of shock environments. First, attenuation with distance is considered. Second, the development and correlation of a model to empirical data was conducted in order to establish modeling best practices and provide a frequency dependent damping schedule that could be used in modeling efforts where data is not available in an effort to reduce model uncertainty in predicting shock response.

Attenuation with distance is considered in an attempt at validating or updating a historical standard that provides knock down factors that can be used to aid in the reduction of high shock environments defined for components that may not feel the full effects of the environment due to their spatial separation from the source of the shock event. To assess this, two sets of test data were analyzed using two methods for which the results were compared to the historical standard developed in the 1960’s based on data collected on technologically obsolete data acquisition systems. The data sets assessed were composed of measurements from two different structural configurations. The first set of data was from a full scale flight like structure simulating a portion of NASA’s Ares I-X vehicle, while the second set comes from a series of tests performed on a flat plate and conducted as part of the same NASA program. The first analysis method followed the historical standard approach such that a direct comparison with the standard could be completed. Here a ratio of the peak shock response spectrum as a function of distance from the source was used. The second approach ratioed an approximate energy calculation in a similar fashion. Both approaches resulted in similar results, with the approximate energy method better aligning with the historical standard. Though there was some agreement with the historical standard, the data generally suggested that the historical standard is not a conservative estimate of attenuation with distance. The variation in the test results, however, was large enough to require further testing to provide an updated standard.

In developing and correlating the model, there were several goals. First, as part of the development and correlation process, any best practices associated with modeling shock response were documented. This included defining a frequency dependent damping schedule that can be used as a basis when modeling other structures for which no data is available. Second, use a wavelet transform in the correlation process. Rather than relying on time history and spectral density comparisons only, a different tool, the harmonic wavelet transform, was used to correlate the model from a time-frequency stand point. Third, the model was used to extrapolate the same structural configuration with different loading conditions to determine how well the correlated damping schedule and overall response characteristics could be simulated using the identified best practices. Finally, an investigation into a split peak response characteristic that was discovered as part of the flat plate data quality review was conducted.

In model development, several best practices could be determined. First, plate elements provided the quickest solution time combined with overall good response characteristics making them the recommend element type. Second, when the load on the structure is due to a linear shaped charge, not including the finite detonation velocity of the charge was determined to alter the response, leading to the recommendation that this be included in future modeling efforts. Third, in defining the applied load, it is best to keep as short as a duration load application as feasible and to use a forcing function shape with a finite rise and fall rate. Lastly a frequency dependent damping schedule was provided for use in other modeling efforts where correlation data may not be available.

The spit peak response characteristic of the flat plate data was determined to be wave reflection from the edge of the plate. This was determined by investigation with the harmonic wavelet, and the realization that the traveling wave speed was not driven by the elastic modulus, but rather the shear modulus.

Three general conclusions can be taken away from this work. First, based on comparison with the available test data, the historical standard should be further investigated. Second, when modeling structural shock response it is important to use as short of a duration forcing function as feasible, incorporate the appropriate detonation velocity of the explosive input when appropriate, and to use a forcing function with a finite rise and fall rate. Furthermore, plate elements provide the best balance of solution time and good response characteristics. Lastly, the harmonic wavelet transform provides a better tool for shock characterization, model correlation, and data investigation than the shock response spectrum. The transform requires no damping assumptions, and it maintains the connection between the time and frequency domains of the forcing function, both of which are not captured when using a shock response spectrum.

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