Some theorems in classical elastodynamic

Applied Mechanics

Wheeler, Lewis Turner ; Sternberg, Eli

University:California Institute of Technology

Department:Engineering and Applied Science

关键词: Applied Mechanics;   

Others  :  https://thesis.library.caltech.edu/9546/1/Wheeler_lt_1969.pdf

美国|英语

来源: Caltech THESIS

【 摘 要 】

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.