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Neil Jerome A. Egarguin

University of Houston

Defect Detection in a One-dimensional Spring-Mass System

February 7, 2019
5:00pm    PGH 646


Detecting defects in physical systems using external or easily accessible measurements had been widely studied in the context of optics, electromagnetism, nanotechnology, metamaterials and other industrial and mechanical applications. Spring-mass systems are commonly used as simple models for some of these physical systems. In this talk, we shall discuss the development of a defect detection scheme in a one-dimensional Hookean spring-mass system. We shall consider a coupled spring-mass system in which the nodes are of unit mass, except for some defective nodes. The goal is to determine the location and/or the mass of the defects using some measurements obtained from the first mass. These measurements involve the longitudinal vibrations due to a unit impulse applied to the first mass.

The scheme we developed relies on the Laplace transform of the system of ODEs modelling the vibrations in the spring-mass system and some optimization techniques. The talk will highlight the derivation of the defect detection strategy, as well as some numerical results. Towards the end of the talk, we shall also look at some possible extensions of this work such as designing algorithms for systems with varying stiffness coefficient and the use of better numerical minimization procedures, and other related research topics for undergraduate students.

This talk is based on a research project with Noam Harari (UH undergraduate student) and Dr. Daniel Onofrei.

Pizza will be served.

A spring-mass system with defect at location j
A spring-mass system with defect at location j

Plot of the residual function showing the location and
      mass of the defect
Plot of the residual function showing the location and mass of the defect

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