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On the dynamics of rods in the theory of Kirchhoff and Clebsch. (English) Zbl 0784.73044
The Kirchhoff-Clebsch theory of inextensible curved rods is generalized to a modern finite deformation theory. The classical starting equations are replaced by a system of six equations in the terms of three components of the force resultant and three Euler angles. This allows the study of motions in which the rod is subjected not only to flexural effects, but also to torsion and twist. Explicit representations of the case of travelling waves with torsion and twist propagating in naturally prismatic rods are derived.

MSC:
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H45 Vibrations in dynamical problems in solid mechanics
74B20 Nonlinear elasticity
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