Title:
Characterization of nonlinearity parameters in an elastic material with quadratic nonlinearity with a complex wave field

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dc.contributor.advisor Jacobs, Laurence J.
dc.contributor.advisor Qu, Jianmin
dc.contributor.author Braun, Michael Rainer en_US
dc.contributor.committeeMember DesRoches, Reginald
dc.contributor.department Civil and Environmental Engineering en_US
dc.date.accessioned 2009-01-22T15:46:26Z
dc.date.available 2009-01-22T15:46:26Z
dc.date.issued 2008-11-19 en_US
dc.description.abstract This research investigates wave propagation in an elastic half-space with a quadratic nonlinearity in its stress-strain relationship. Different boundary conditions on the surface are considered that result in both one- and two-dimensional wave propagation problems. The goal of the research is to examine the generation of second-order frequency effects and static effects which may be used to determine the nonlinearity present in the material. This is accomplished by extracting the amplitudes of those effects in the frequency domain and analyzing their dependency on the third-order elastic constants (TOEC). For the one-dimensional problems, both analytical approximate solutions as well as numerical simulations are presented. For the two-dimensional problems, numerical solutions are presented whose dependency on the material's nonlinearity is compared to the one-dimensional problems. The numerical solutions are obtained by first formulating the problem as a hyperbolic system of conservation laws, which is then solved numerically using a semi-discrete central scheme. The numerical method is implemented using the package CentPack. In the one-dimensional cases, it is shown that the analytical and numerical solutions are in good agreement with each other, as well as how different boundary conditions may be used to measure the TOEC. In the two-dimensional cases, it is shown that there exist comparable dependencies of the second-order frequency effects and static effects on the TOEC. Finally, it is analytically and numerically investigated how multiple reflections in a plate can be used to simplify measurements of the material nonlinearity in an experiment. en_US
dc.description.degree M.S. en_US
dc.identifier.uri http://hdl.handle.net/1853/26566
dc.publisher Georgia Institute of Technology en_US
dc.subject Nonlinearity parameter en_US
dc.subject Nonlinear wave propagation en_US
dc.subject Reflection en_US
dc.subject Stress-free boundary en_US
dc.subject Rigid boundary en_US
dc.subject Static effects en_US
dc.subject Numerical solution en_US
dc.subject Conservation law en_US
dc.subject Traction boundary condition en_US
dc.subject Higher-order effects en_US
dc.subject Perturbation en_US
dc.subject Material nonlinearity en_US
dc.subject Analytical solution en_US
dc.subject.lcsh Wave-motion, Theory of
dc.subject.lcsh Nonlinear theories
dc.subject.lcsh Ultrasonic testing
dc.subject.lcsh Microstructure
dc.title Characterization of nonlinearity parameters in an elastic material with quadratic nonlinearity with a complex wave field en_US
dc.type Text
dc.type.genre Thesis
dspace.entity.type Publication
local.contributor.advisor Jacobs, Laurence J.
local.contributor.corporatename School of Civil and Environmental Engineering
local.contributor.corporatename College of Engineering
relation.isAdvisorOfPublication 5af40958-ece2-4a76-b071-5ba4c6d99d80
relation.isOrgUnitOfPublication 88639fad-d3ae-4867-9e7a-7c9e6d2ecc7c
relation.isOrgUnitOfPublication 7c022d60-21d5-497c-b552-95e489a06569
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