This work addresses the linear elastic analysis of axisymmetric wave propagation in a finite elastic cylinder. The waves are generated by the Fast Triaxial Device (FTRXD), which fails soil specimens at very rapid rates. The very short duration of the triaxial tests requires the consideration of wave phenomena in the analysis of the test results.
The soil specimens are modeled as linear elastic cylinders which are compressed in the axial direction. The resulting axisymmetric waves are analyzed with the wave equations which are cast in finite difference form, allowing the solution of displacements and stresses throughout the cylinder as a function of time. The validity of the axisymmetric (two-dimensional) analysis is verified by comparing its results to the exact solution of Pochhammer's equations, and by verifying the proper solution of boundary conditions.
A one-dimensional wave analysis of the FTRXD has been completed by Carroll and has proven to closely predict the FTRXD results found in the laboratory. The one-dimensional and two-dimensional analysis results are compared in an effort to identify the FTRXD loading rates, the specimen properties, or the specimen geometries for which the one-dimensional analysis may not be adequate.
Of the variety of parameters considered, only Poisson's ratio is found to have a significant impact when comparing the one-dimensional and two-dimensional analysis results. Also, some significant wave phenomena not apparent in a one-dimensional analysis are observed in the two-dimensional analysis at very high loading rates. But these loading rates are not presently attained in the actual FTRXD testing. Furthermore, for most of the parameters considered, much of the largest differences between the two analyses can be attributed to a difference in time scales used in the two analyses. Thus, at least in the linear elastic range, the one-dimensional analysis appears to adequately predict FTRXD results for present loading rates. Further consideration should be given to the non-linear, two-dimensional analysis and to an appropriate time scale on which the one-dimensional and two-dimensional analyses should be compared.
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Carroll, William F.
Master of Science (M.S.)
College of Engineering
Civil Engineering and Environmental Sciences
Length of Campus-only Access
Masters Thesis (Open Access)
Dissertations, Academic -- Engineering; Engineering -- Dissertations, Academic
Johnson, Brian D., "Axisymmetric wave propagation in a finite linear elastic cylinder" (1988). Retrospective Theses and Dissertations. 4293.