Axially Symmetric Transient Wave Propagation in Elastic Rods with Nonuniform Section.
GRUMMAN AEROSPACE CORP BETHPAGE N Y RESEARCH DEPT
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A one dimensional approximate theory is derived for an elastic circular rod with nonuniform cross section. Three coupled equations, taking into account the longitudinal, radial, and axial shear deformations and their inertias, are obtained as an extension of the Mindlin-McNiven theory to the case of nonuniform rods. Responses of both the semi-infinite rod and finite rod with elastic end support due to either a step or a pulse loading are studied by the method of characteristics. Calculated results such as stresses versus time for different stations along the rod and stresses as functions of distance for instants of time are presented and compared for several cases. The geometrical effect of the variation of section on the stresses and velocities and the effect of the elastic support on the reflection and propagation of the stress waves are deduced. Author