Some Theorems in Classical Elastodynamics

Citation

Wheeler, Lewis Turner (1969) Some Theorems in Classical Elastodynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/N9HD-N641. https://resolver.caltech.edu/CaltechTHESIS:01252016-143403275

Abstract

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.

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