Citation
Jeffers, Robert Humphrey Francis (1971) On TwoDimensional Waves of Finite Amplitude in Elastic Materials of Harmonic Type. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:09272017154819290
Abstract
In this thesis, twodimensional waves of finite amplitude in elastic materials of harmonic type are considered. After specializing the basic equations of finite elasticity to these materials, attention is restricted to plane motions and a new representation theorem (analogous to the theorem of Lamé in classical linear elasticity) for the displacements in terms of two potentials is derived.
The twodimensional problem of the reflection of an obliquely incident periodic wave from the free surface of a halfspace composed of an elastic material of harmonic type is formulated. The incident wave is a member of a special class of exact onedimensional solutions of the nonlinear equations for elastic materials of harmonic type, and reduces upon linearization to the classical periodic "shear wave" of the linear theory.
A perturbation procedure for the construction of an approximate solution of the reflection problem, for the case where the incident wave is of small but finite amplitude, is constructed. The procedure involves series expansions in powers of the ration of the amplitude to the wavelength of the incident wave and is of the socalled twovariable type. The perturbation scheme is carried far enough to determine the secondorder corrections to the linearized theory.
A summary of results for the reflection problem is provided, in which nonlinear effects on the reflection pattern, on the particle displacements at the free surface and on the behavior at large depth in the halfspace are detailed.
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): 
 
Thesis Committee: 
 
Defense Date:  6 August 1970  
Funders: 
 
Record Number:  CaltechTHESIS:09272017154819290  
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:09272017154819290  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  10466  
Collection:  CaltechTHESIS  
Deposited By:  Benjamin Perez  
Deposited On:  28 Sep 2017 17:30  
Last Modified:  28 Sep 2017 17:30 
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