Browsing by Author "Egarguin, Neil Jerome"
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Item Defect Analysis of 1D Spring-Mass Systems via Laplace Transform and Asymptotics(2019) Guan, Larry; Egarguin, Neil JeromeSpring-mass systems have seen utility for decades in modeling multiple physical phenomena like elastic deformation and wave propagation. Particularly, we focus on linear spring-mass systems and use experimental data to analytically locate and enumerate defects along the chain. We begin by taking the differential equations describing an almost uniform spring-mass system with a predetermined number of blocks into the Laplace domain; there is an arbitrary number of “error” masses somewhere along the chain with higher or lower mass than the remaining blocks. Application of elementary algebra and asymptotic analysis enables us to numerically test each block for defect status using the vibrational data of only the first block in the chain while simultaneously counting the number of defects. However, despite the sound nature of the theory, this process works only for data without measurement/numerical noise and defects beyond the first are undetectable.Item On Passive Backscatter Cloaking In One Dimensional Oscillation Phenomena(2020-09-29) Spencer, Damon; Egarguin, Neil JeromeBackscattered cloaking attempts to mask vibrations in the direction of measurement. This research focuses on one dimensional backscattered cloaking. This problem can be described in terms of spring mass mechanics, circuits, acoustics, and atomic lattice vibrations. In this poster, we discuss methods for cloaking both a ten mass system toy problem and a large one hundred mass system. We utilize Plancherel’s theorem to allow optimization of both systems in the Fourier domain. We then proceed to optimize the ten mass system using a Fourier transform polynomial and the hundred mass system using Tikhonov regularization. Simulation results are provided, and results show a large improvement in the residual value from optimizing both the ten and one hundred mass systems. The results also show that the residual value decreases significantly in dissipative media, and an explanation for why this is true is provided. Overall, we find that cloaking can be done well at a large scale using Tikhonov regularization.Item Two Approaches for Optimal Synthesis of a Thin Wire Antenna(2019) Fegan, Lance; Egarguin, Neil JeromeIn this study, we explore a strategy for determining the current distribution of a thin-wire antenna based on a given radiation pattern. By this we mean seeking for a current distribution on the antenna so that the generated radiation pattern closely approximates a prescribed far field pattern. The integral equation that models the relationship between the current distribution and the generated radiation pattern was analyzed using the method of moments. The unknown current distribution was approximated with a truncated series leading to a system of linear equations. This linear system is then solved using Tikhonov regularization. This study directly compares the results obtained from two series representations, namely the Taylor and Fourier series. Our results show that the accuracy of this strategy is primarily dependent upon the approximating series used. The results from this study has potential applications in radar and radar defense technologies. Further research on this problem may lead to the development of more effective techniques in terms of accuracy and stability.