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Self-similar elastodynamic solutions for the plane wedge


Wojcik, Gregory Lynn (1977) Self-similar elastodynamic solutions for the plane wedge. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/E1D3-0T11.


Wave propagation in a two-dimensional elastic wedge is fundamental to a large class of problems in elastodynamic theory, however until now analytical solutions to all but certain degenerate cases were unknown. In this thesis a general elastodynamic solution is derived for the wedge in a state of plane strain. Surface tractions are, restricted to uniform normal and shear loads spreading from the wedge vertex at constant velocity. The geometry and loading then allow self-similar solutions of the governing differential equations and boundary conditions in hyperbolic and elliptic domains. Hyperbolic solutions are found in terms of the elliptic solutions by the method of characteristics, while elliptic solutions are reduced using analytic function theory to two independent Fredholm integral equations of the second kind in one dimension. Although numerical solutions are beyond the scope of the investigation, the integral equations are solvable by standard techniques. Such solutions can be used to solve a number of plane elastodynamic problems involving an edge.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Sechler, Ernest Edwin (advisor)
  • Babcock, Charles D. (advisor)
Thesis Committee:
  • Sechler, Ernest Edwin (chair)
  • Babcock, Charles D.
  • Knowles, James K.
  • Miklowitz, Julius
Defense Date:9 May 1977
Record Number:CaltechETD:etd-11132006-080224
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4533
Deposited By: Imported from ETD-db
Deposited On:12 Dec 2006
Last Modified:21 Dec 2019 02:24

Thesis Files

PDF (Wojcik_gl_1977.pdf) - Final Version
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