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Semi-Analytical Finite Element method for guided waves in civil engineering plate-like structures

Nielsen, Christian LU (2015) VTG820 20151
Engineering Geology
Civil Engineering (M.Sc.Eng.)
Abstract
Guided waves have a signicant potential for Structural Health Monitoring (SHM) and Non-Destructive Testing (NDT) due to their relatively long distance of propagation and sensitivity to discontinuities along the propagation path, anywhere through the material thickness. The inability to model wave guides of arbitrary cross-section using current matrix methods, has led to the development of a technique called Semi-Analytical Finite Element (SAFE). In civil engineering it is of considerable interest to study guided waves in plates and plate-like structures: such as foundations, embankments, reactor enclosures and dams. NDT have potential as an essential tool in the life cycle management of the built environment: from preliminary... (More)
Guided waves have a signicant potential for Structural Health Monitoring (SHM) and Non-Destructive Testing (NDT) due to their relatively long distance of propagation and sensitivity to discontinuities along the propagation path, anywhere through the material thickness. The inability to model wave guides of arbitrary cross-section using current matrix methods, has led to the development of a technique called Semi-Analytical Finite Element (SAFE). In civil engineering it is of considerable interest to study guided waves in plates and plate-like structures: such as foundations, embankments, reactor enclosures and dams. NDT have potential as an essential tool in the life cycle management of the built environment: from preliminary investigations, verication of new structures to its maintenance and, nally, demolition. In this master's thesis the semi-analytical nite element method is reviewed, implemented and studied for civil engineering plate-like structures using the commercial nite element software COMSOL. First, a review of SAFE and its underlying concepts, such as solid mechanics, Lamb waves and quadratic eigenvalue problems, is presented. Second, its implementation, using a coecient form Partial Dierential Equation (PDE) formalism in COMSOL's mathematical modelling environment, is presented. Third, SAFE is applied to four civil engineering problems: (1) a continuous homogeneous isotropic linear elastic free plate, (2) a continuous homogeneous isotropic linear elastic free plate with proportional hysteretic damping, (3) a continuous isotropic linear elastic free plate with a stiness gradient and (4) a multi-layered half-space. The SAFE model solution is curve tted to synthetic data from the matrix method software DISPERSE. 3 It is found that SAFE successfully predicts the dispersion relations for the enumerated civil engineering structures. Furthermore, it is shown that exploiting the underlying eigenvalues and eigenvectors, extended properties such as attenuation, lossless excitability and energy velocity may be predicted using a SAFE formulation. Moreover, it is shown that introducing light damping to a free plate results in negligible changes in phase velocities. Furthermore, it is shown that a stiness gradient over the plate thickness have small eects on the S1 zero group velocity frequency. (Less)
Popular Abstract (Swedish)
Seismisk undersökning stärker förvalt-ningen av den byggda miljön
Den byggda miljön är full av plattor: t.ex. bjälklag, grunder och vägbanor. Nya algoritmer för utvärdering av seismiska undersökningar öppnar dörrar för att modellera plattor med mer komplicerade geometrier. Genom-förda simuleringar visar att t.ex. väg-banor kan modelleras enkelt.
Författare: Christian Nielsen Examensarbete: Semi-Analytical Finite Element method for guided waves in civil engineering plate-like strucutures – Simu-lering av platt-seismik i COMSOL baserad på en semi-analytisk approximation av vågekva-tionen.
Avd. Teknisk geologi, Lunds tekniska
högskola
Förvaltningen av den byggda miljön är en betydande utmaning för bygg-branschen. För att prioritera var... (More)
Seismisk undersökning stärker förvalt-ningen av den byggda miljön
Den byggda miljön är full av plattor: t.ex. bjälklag, grunder och vägbanor. Nya algoritmer för utvärdering av seismiska undersökningar öppnar dörrar för att modellera plattor med mer komplicerade geometrier. Genom-förda simuleringar visar att t.ex. väg-banor kan modelleras enkelt.
Författare: Christian Nielsen Examensarbete: Semi-Analytical Finite Element method for guided waves in civil engineering plate-like strucutures – Simu-lering av platt-seismik i COMSOL baserad på en semi-analytisk approximation av vågekva-tionen.
Avd. Teknisk geologi, Lunds tekniska
högskola
Förvaltningen av den byggda miljön är en betydande utmaning för bygg-branschen. För att prioritera var åt-gärder bör göras krävs besiktningar där storleken och betydelsen av felet kan avgöras. En sådan metod är seismik. Inom seismiken använder man vibrationer för att utvärdera skador och brister i konstruktionen.
Vid undersökning av plattor uppstår en speciell typ av vibrationer: Lamb-vågor. De är attraktiva att använda vid besiktning, då de kan färdas långa sträckor i konstruktionen. Därmed kan man undersöka en stör-re del av konstruktionen från en gi-ven mätpunkt. Lambvågor är också relativt känsliga för skador, d.v.s. att vågens utbredning ändras vid en skada, och därmed kan användas för skadebesiktning.
Den numeriska metoden Semi-Analytical Finite Element (SAFE) kan användas för att skapa modeller över hur vågutbredningen sker i plattor. Därmed kan man relatera uppmätta vibrationer till olika kon-struktions koncept, som t.ex. skador.
Examensarbetets mål har varit att skapa bättre förståelse för hur SAFE kan användas för att modellera olika typer konstruktioner. Först presen-teras en litteraturstudie över de grundläggande matematiska sam-banden. Därefter undersöks fyra fallstudier: (1) en betong platta, (2) en betong platta med material dämpning, (3) en betong platta med styvhetsgradient och (4) en vägkon-struktion.
Resultaten från simuleringarna visar att SAFE kan användas för utvärde-ring, med samma noggrannhet som nuvarande metoder. Men med förde-len att den tillåter mer komplicerade geometrier på plattan än övriga motsvarande metoder. (Less)
Please use this url to cite or link to this publication:
author
Nielsen, Christian LU
supervisor
organization
alternative title
Semianalytisk finita element metoden för platt-liknande vågledare inom strukturmekaniken
course
VTG820 20151
year
type
H3 - Professional qualifications (4 Years - )
subject
keywords
seismics, structural health monitoring, lamb waves, SAFE, semi analytical finite element, wave guide finite element, non destructive testing, civil engineering, ultrasound, ultrasonography, comsol, wave guide, plate
report number
TVTG-5140
other publication id
LUTVDG / (TVTG-5140) / 1-86 (2015)
language
English
additional info
Examinor: Peter Ulriksen
id
7440322
date added to LUP
2015-06-24 13:43:55
date last changed
2015-06-24 13:43:55
@misc{7440322,
  abstract     = {Guided waves have a signicant potential for Structural Health Monitoring (SHM) and Non-Destructive Testing (NDT) due to their relatively long distance of propagation and sensitivity to discontinuities along the propagation path, anywhere through the material thickness. The inability to model wave guides of arbitrary cross-section using current matrix methods, has led to the development of a technique called Semi-Analytical Finite Element (SAFE). In civil engineering it is of considerable interest to study guided waves in plates and plate-like structures: such as foundations, embankments, reactor enclosures and dams. NDT have potential as an essential tool in the life cycle management of the built environment: from preliminary investigations, verication of new structures to its maintenance and, nally, demolition. In this master's thesis the semi-analytical nite element method is reviewed, implemented and studied for civil engineering plate-like structures using the commercial nite element software COMSOL. First, a review of SAFE and its underlying concepts, such as solid mechanics, Lamb waves and quadratic eigenvalue problems, is presented. Second, its implementation, using a coecient form Partial Dierential Equation (PDE) formalism in COMSOL's mathematical modelling environment, is presented. Third, SAFE is applied to four civil engineering problems: (1) a continuous homogeneous isotropic linear elastic free plate, (2) a continuous homogeneous isotropic linear elastic free plate with proportional hysteretic damping, (3) a continuous isotropic linear elastic free plate with a stiness gradient and (4) a multi-layered half-space. The SAFE model solution is curve tted to synthetic data from the matrix method software DISPERSE. 3 It is found that SAFE successfully predicts the dispersion relations for the enumerated civil engineering structures. Furthermore, it is shown that exploiting the underlying eigenvalues and eigenvectors, extended properties such as attenuation, lossless excitability and energy velocity may be predicted using a SAFE formulation. Moreover, it is shown that introducing light damping to a free plate results in negligible changes in phase velocities. Furthermore, it is shown that a stiness gradient over the plate thickness have small eects on the S1 zero group velocity frequency.},
  author       = {Nielsen, Christian},
  keyword      = {seismics,structural health monitoring,lamb waves,SAFE,semi analytical finite element,wave guide finite element,non destructive testing,civil engineering,ultrasound,ultrasonography,comsol,wave guide,plate},
  language     = {eng},
  note         = {Student Paper},
  title        = {Semi-Analytical Finite Element method for guided waves in civil engineering plate-like structures},
  year         = {2015},
}