Damage modeling and damage detection for structures using a perturbation method

This thesis is about using structural-dynamics based methods to address the existing challenges in the field of Structural Health Monitoring (SHM). Particularly, new structural-dynamics based methods are presented, to model areas of damage, to do damage diagnosis and to estimate and predict the sens...

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Main Author: Dixit, Akash
Published: Georgia Institute of Technology 2012
Subjects:
Online Access:http://hdl.handle.net/1853/43575
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spelling ndltd-GATECH-oai-smartech.gatech.edu-1853-435752013-01-07T20:38:50ZDamage modeling and damage detection for structures using a perturbation methodDixit, AkashPerturbation methodDamage modelingVibration based structural health monitoringDamage identificationTimoshenko beam theoryEuler-Bernoulli beam theoryPartial mode contribution methodKirchhoff's plate theoryStructural health monitoringPerturbation (Mathematics)Fracture mechanicsNondestructive testingThis thesis is about using structural-dynamics based methods to address the existing challenges in the field of Structural Health Monitoring (SHM). Particularly, new structural-dynamics based methods are presented, to model areas of damage, to do damage diagnosis and to estimate and predict the sensitivity of structural vibration properties like natural frequencies to the presence of damage. Towards these objectives, a general analytical procedure, which yields nth-order expressions governing mode shapes and natural frequencies and for damaged elastic structures such as rods, beams, plates and shells of any shape is presented. Features of the procedure include the following: 1. Rather than modeling the damage as a fictitious elastic element or localized or global change in constitutive properties, it is modeled in a mathematically rigorous manner as a geometric discontinuity. 2. The inertia effect (kinetic energy), which, unlike the stiffness effect (strain energy), of the damage has been neglected by researchers, is included in it. 3. The framework is generic and is applicable to wide variety of engineering structures of different shapes with arbitrary boundary conditions which constitute self adjoint systems and also to a wide variety of damage profiles and even multiple areas of damage. To illustrate the ability of the procedure to effectively model the damage, it is applied to beams using Euler-Bernoulli and Timoshenko theories and to plates using Kirchhoff's theory, supported on different types of boundary conditions. Analytical results are compared with experiments using piezoelectric actuators and non-contact Laser-Doppler Vibrometer sensors. Next, the step of damage diagnosis is approached. Damage diagnosis is done using two methodologies. One, the modes and natural frequencies that are determined are used to formulate analytical expressions for a strain energy based damage index. Two, a new damage detection parameter are identified. Assuming the damaged structure to be a linear system, the response is expressed as the summation of the responses of the corresponding undamaged structure and the response (negative response) of the damage alone. If the second part of the response is isolated, it forms what can be regarded as the damage signature. The damage signature gives a clear indication of the damage. In this thesis, the existence of the damage signature is investigated when the damaged structure is excited at one of its natural frequencies and therefore it is called ``partial mode contribution". The second damage detection method is based on this new physical parameter as determined using the partial mode contribution. The physical reasoning is verified analytically, thereupon it is verified using finite element models and experiments. The limits of damage size that can be determined using the method are also investigated. There is no requirement of having a baseline data with this damage detection method. Since the partial mode contribution is a local parameter, it is thus very sensitive to the presence of damage. The parameter is also shown to be not affected by noise in the detection ambience.Georgia Institute of Technology2012-06-06T16:42:52Z2012-06-06T16:42:52Z2012-01-06Dissertationhttp://hdl.handle.net/1853/43575
collection NDLTD
sources NDLTD
topic Perturbation method
Damage modeling
Vibration based structural health monitoring
Damage identification
Timoshenko beam theory
Euler-Bernoulli beam theory
Partial mode contribution method
Kirchhoff's plate theory
Structural health monitoring
Perturbation (Mathematics)
Fracture mechanics
Nondestructive testing
spellingShingle Perturbation method
Damage modeling
Vibration based structural health monitoring
Damage identification
Timoshenko beam theory
Euler-Bernoulli beam theory
Partial mode contribution method
Kirchhoff's plate theory
Structural health monitoring
Perturbation (Mathematics)
Fracture mechanics
Nondestructive testing
Dixit, Akash
Damage modeling and damage detection for structures using a perturbation method
description This thesis is about using structural-dynamics based methods to address the existing challenges in the field of Structural Health Monitoring (SHM). Particularly, new structural-dynamics based methods are presented, to model areas of damage, to do damage diagnosis and to estimate and predict the sensitivity of structural vibration properties like natural frequencies to the presence of damage. Towards these objectives, a general analytical procedure, which yields nth-order expressions governing mode shapes and natural frequencies and for damaged elastic structures such as rods, beams, plates and shells of any shape is presented. Features of the procedure include the following: 1. Rather than modeling the damage as a fictitious elastic element or localized or global change in constitutive properties, it is modeled in a mathematically rigorous manner as a geometric discontinuity. 2. The inertia effect (kinetic energy), which, unlike the stiffness effect (strain energy), of the damage has been neglected by researchers, is included in it. 3. The framework is generic and is applicable to wide variety of engineering structures of different shapes with arbitrary boundary conditions which constitute self adjoint systems and also to a wide variety of damage profiles and even multiple areas of damage. To illustrate the ability of the procedure to effectively model the damage, it is applied to beams using Euler-Bernoulli and Timoshenko theories and to plates using Kirchhoff's theory, supported on different types of boundary conditions. Analytical results are compared with experiments using piezoelectric actuators and non-contact Laser-Doppler Vibrometer sensors. Next, the step of damage diagnosis is approached. Damage diagnosis is done using two methodologies. One, the modes and natural frequencies that are determined are used to formulate analytical expressions for a strain energy based damage index. Two, a new damage detection parameter are identified. Assuming the damaged structure to be a linear system, the response is expressed as the summation of the responses of the corresponding undamaged structure and the response (negative response) of the damage alone. If the second part of the response is isolated, it forms what can be regarded as the damage signature. The damage signature gives a clear indication of the damage. In this thesis, the existence of the damage signature is investigated when the damaged structure is excited at one of its natural frequencies and therefore it is called ``partial mode contribution". The second damage detection method is based on this new physical parameter as determined using the partial mode contribution. The physical reasoning is verified analytically, thereupon it is verified using finite element models and experiments. The limits of damage size that can be determined using the method are also investigated. There is no requirement of having a baseline data with this damage detection method. Since the partial mode contribution is a local parameter, it is thus very sensitive to the presence of damage. The parameter is also shown to be not affected by noise in the detection ambience.
author Dixit, Akash
author_facet Dixit, Akash
author_sort Dixit, Akash
title Damage modeling and damage detection for structures using a perturbation method
title_short Damage modeling and damage detection for structures using a perturbation method
title_full Damage modeling and damage detection for structures using a perturbation method
title_fullStr Damage modeling and damage detection for structures using a perturbation method
title_full_unstemmed Damage modeling and damage detection for structures using a perturbation method
title_sort damage modeling and damage detection for structures using a perturbation method
publisher Georgia Institute of Technology
publishDate 2012
url http://hdl.handle.net/1853/43575
work_keys_str_mv AT dixitakash damagemodelinganddamagedetectionforstructuresusingaperturbationmethod
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