Chapter 12 Development of a Mapping Function for a Low- to High-Amplitude Input Joshua H. Campbell, Janet C. Wolfson, Jacob C. Dodson, Alain L. Beliveau, Jonathan Hong, and Greg Falbo Abstract The Air Force Research Laboratory is continuing research to design a controllable pyroshock test to excite a test item over the entire frequency spectrum from low (10 Hz) to high (10 kHz) at different forcing levels. When a linear Frequency Response Function exists we would expect that we can design a multiple input test to achieve a desired output response based on superposition of the single input modal response of the test structure. Experimental modal analysis is performed to evaluate the differences in FRF’s for the different input force levels generated by a modal hammer and a detonator. The final outcome of this research endeavor is to be able to perform a modal analysis on the test platform and use that information to define the input force location, magnitude, and time delay to achieve a desired output response. Initial studies at the output location will focus on utilizing the Shock Response Spectrum as the Figure of Merit, however, energy methods and other criteria may be considered. This paper will present progress in the development of the Design-a-Shock method and the difficulties that were encountered in trying to capture the input response of a detonator, the lessons learned from the testing, and a discussion on the characterization of the system response. Keywords Bookshelf • Mapping • Simultaneous • Modal • Multi-axial 12.1 Introduction The idea behind the Design-a-Shock is to determine if a relationship exists between an input from a force hammer and an input from a pyroshock event (detonator, multiple detonators, and pellet sized explosives) in the elastic range. The desire is to develop a scientific, repeatable, field experiment that can reproduce the desired forces in order to determine the failure mechanisms in the systems under test. A new test article was proposed and an initial computational study was performed and reported at the Society of Experimental Mechanic’s IMAC XXVIII [1]. The analytical results were then compared to a near-field pyroshock test. This analysis led to the development of the Multi-Axial Pyroshock Plate (MAPP) test set-up. Initial pyroshock tests were performed on the MAPP test set-up where acceleration time histories were captured and Shock Response Spectra (SRS) were calculated. The success of the tests was determined by comparing the SRS from the tests with a desired SRS band. These initial tests show that the technology could simulate aspects of the SRS, however, the application of the pyroshock needed further refinement. In order to determine the optimum placement of pyroshock inputs an initial test series was developed to compare simple modal impacts to more complex near-field pyroshock inputs. A series of laboratory tests were performed on a sub-scale aluminum plate and the more complex full-scale MAPP test article. These tests involved using an impact hammer (input force) at different locations and capturing the frequency domain data at a variety of locations along a grid. The initial sub-scale laboratory tests focused on a specific input at 32 different locations and four output locations. Acceleration time histories were captured at each location. From that data the Frequency Response Functions J.H. Campbell ( ) • J.C. Wolfson • J.C. Dodson Air Force Research Laboratory, AFRL/RWMF; 306 W. Eglin Blvd., Bldg. 432, 32542-5430 Eglin AFB, FL, USA e-mail: joshua.campbell.28@eglin.af.mil A.L. Beliveau • J. Hong Applied Research Associates, Inc., 956 W John Sims Pkwy, Niceville, FL 32578, USA e-mail: alain.beliveau.ctr@us.af.mil G. Falbo LMS Americas, 5755 New King Drive Troy, MI 48098, USA e-mail: greg.falbo@siemens.com © The Society for Experimental Mechanics, Inc. 2015 A. Wicks (ed.), Shock & Vibration, Aircraft/Aerospace, and Energy Harvesting, Volume 9, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-15233-2_12 115
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