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Planar travelling waves in incompressible elastic rods. (English) Zbl 1134.74378

Summary: This paper first describes the rich and intricate structure of the hyperbolic equations governing the planar motions of incompressible nonlinearly elastic rods. It then shows that under a variety of constitutive restrictions, these equations have periodic travelling-wave solutions coupling longitudinal and transverse extension, flexure, and shear.

MSC:

74J30 Nonlinear waves in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
74B20 Nonlinear elasticity
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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