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.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/26566 |
| Date | 19 November 2008 |
| Creators | Braun, Michael Rainer |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Detected Language | English |
| Type | Thesis |
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