Abstract
A non-classical theory of elastic rods of uniform cross sections, descriptive of wave propagation and vibrations, is constructed within the scope of the theory of Cosserat elasticity. A separation of variables solution is sought for the three-dimensional field equations, and a generalized variational theorem is used in the analysis. The effects of transverse shear and normal strains as well as those of rotatory inertia are taken into account. The microrotational motions give rise to new type of waves not present in any of the known rod theories. In particular, the nature of extensional waves is discussed and the uniqueness of solution is established. The results are valid for both nonpolar and Cosserat rods, and contain those of earlier theories as special cases. [Supported by the Office of Naval Research.]
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