טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentZach Glikman
SubjectMechanical Behavior of a Fiber-Optic Embedded in a
Deterministic and Stochastic Heterogeneous Matrix
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Emeritus Altus Eli


Abstract

The deterministic and probabilistic response of fiber optic sensors embedded in stochastically heterogeneous, linear elastic structure is developed, using the new Functional Perturbation Method (FPM).

The method is based on considering the unknown fields such as strain and displacements, as functionals of the non-uniform property, i.e., elastic modules. The governing differential equation is expanded functionally by a Fréchet series, leading to a set of differential equations with constant coefficients, from which the unknown strain field is found successively to any desirable degree of accuracy. A unique property of the FPM is that once the Fréchet derivatives are found, the solution for any morphology is obtained by direct integration, without re-solving the differential equation for each case.

The method was used to analyze two different, but related engineering problems: first, the influence of statistical modulus field on sensor output and second, the effect of local modulus disorder (damage like) on fiber output.

In addition, a new "Shape Method" - an analytical way of describing module disorder by its relative location, area and moment of inertia, was developed in order to find the characteristic of a modulus disorder located between two fiber sensor stations.

Advantages of the method are a.) There is no need to integrate Fréchet functions and b.) Once sensor stations outputs are detected, disorder area and location can be calculated by a simple formula.  

The FPM series and Shape method are powerful tools in analyzing sensors output for local heterogeneous fields related to health monitoring. The differences between the methods are discussed, as well as advantages and limitations.