Solitary shock waves and other travelling waves in a general compressible hyperelastic rod. (English) Zbl 1004.74046

Dai, Hui-Hui; Huo, Yi

Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 456, No. 1994, 331-363 (2000).

The authors demonstrate the existence of solitary and shock waves not only in the case of incompressible hyperelastic rods, but also in the case of compressible rods. The governing equations are derived, and then long waves as well as finite-length waves are considered. For various travelling waves, the authors give representations in phase plane. A new phenomenon is put into evidence: namely, a solitary wave can suddenly change into a periodic wave (with finite period), which is interpreted as a sudden transformation of a homoclinic orbit into a classic orbit.

Reviewer: Petre P.Teodorescu (Bucureşti)

MSC:

74J40	Shocks and related discontinuities in solid mechanics
74K10	Rods (beams, columns, shafts, arches, rings, etc.)
74B20	Nonlinear elasticity

Keywords:

solitary shock waves; compressible hyperelastic rod; travelling waves; sudden wave transformation; phase plane representation; long waves; finite-length waves; homoclinic orbit