Date of Award


Document Type

Open Access Master's Thesis

Degree Name

Master of Science in Mechanical Engineering (MS)

Administrative Home Department

Department of Mechanical Engineering-Engineering Mechanics

Advisor 1

Jason R. Blough

Committee Member 1

Charles Van Karsen

Committee Member 2

James DeClerck


Resonant plate pyroshock tests only offer to test one component axis at a time, while the qualification pyroshock tests often have three single-axis specifications to meet. There is an interest in creating a multi-axis test environment from the single-axis resonant plate parts to save testing time, create a more realistic test environment, and monitor the possibility of an overtest. To investigate this, LaGrange-multiplier frequency based substructuring was implemented to virtually arrange the single-axis resonant plate subsystems into different assembly configurations and mathematically calculate the new assembly dynamics. A shock response spectrum was calculated from the new assembly dynamics through an inverse Fourier transform and convolved with a simple shock pulse. Three objective functions were designated to minimize the difference between the in-axis and off-axis response magnitudes of the shock response spectrum over three frequency ranges. These objective functions included the root mean square, the sum of the square of the residuals, and absolute difference. This process of frequency based substructuring, to shock response spectrum, and to objective function calculation was repeated iteratively for 22 possible new assembly configurations, each with five possible response locations. The resulting assembly of the minimized objective function satisfied the requirements of in-axis and off-axis responses close in magnitude and within the shock test tolerance bands of +/- 6 dB. The iterative optimization process was performed on finite element model data, and three configurations were verified experimentally through full assembly modal tests and through experimental frequency based substructuring.