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Neutral stability of compression solitons at bending of nonlinear elastic rod. (Russian, English) Zbl 1177.74213
Prikl. Mat. Mekh. 72, No. 3, 466-476 (2008); translation in J. Appl. Math. Mech. 72, No. 3, 323-330 (2008).
For the description of interaction of longitudinal and bending waves in a rod a system of equations of isotropic elasticity theory is applied with allowance for nonlinear corrections with regard to the interaction. This system of equations describes long longitudinal bending waves of small but finite amplitude. It is shown that there exist captured bending moda propagating together with the compression soliton. It is established that these moda, being the less stable ones, do not grow with time.
MSC:
74J35 Solitary waves in solid mechanics
74K05 Strings
Software:
MODA
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References:
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