Intense bending waves in a bar (Q1370275)

This paper deals with nonlinear (bending and longitudinal) vibrations and wave propagation in thin bars. It is an extension of a previous paper by the author and \textit{A. I. Potapov} [Arch. Appl. Mech. 66, No. 3, 168-176 (1996; Zbl 0841.73035)] which takes into account higher-order approximations of nonlinear effects. It is shown that: (1) if the group velocity of a bending wave train is smaller than that of longitudinal waves, self-modulation slowly developing during propagation may occur (instability and creation of soliton-like envelopes); (2) if it is greater, no self-modulation takes place (stability); (3) in the transmission zone the system changes its stability behaviour, and the group matching of quasiharmonic bending waves appears together with a nearly uniform longitudinal deformation. Partly deficient English.