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Some theorems in classical elastodynamic


Wheeler, Lewis Turner (1969) Some theorems in classical elastodynamic. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/N9HD-N641.


This investigation is concerned with various fundamental aspects of the linearized dynamical theory for mechanically homogeneous and isotropic elastic solids. First, the uniqueness and reciprocal theorems of dynamic elasticity are extended to unbounded domains with the aid of a generalized energy identity and a lemma on the prolonged quiescence of the far field, which are established for this purpose. Next, the basic singular solutions of elastodynamics are studied and used to generate systematically Love's integral identity for the displacement field, as well as an associated identity for the field of stress. These results, in conjunction with suitably defined Green's functions, are applied to the construction of integral representations for the solution of the first and second boundary-initial value problem. Finally, a uniqueness theorem for dynamic concentrated-load problems is obtained.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mechanics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Sternberg, Eli
Thesis Committee:
  • Unknown, Unknown
Defense Date:28 June 1968
Record Number:CaltechTHESIS:01252016-143403275
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9546
Deposited On:25 Jan 2016 23:51
Last Modified:21 Dec 2019 01:32

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