THE EFFECT OF THE ELASTIC NONLINEARITY AND WARPING ON THE PARAMETERS OF THE TORSIONAL WAVE PROPAGATING IN THE THIN-WALLED ROD

Abstract

A mathematical model describing the propagation of torsional wave in the rod, including geometric and material elastic nonlinearity and deplanation, i.e. the output of the cross-section, in the deformation process of the rod, from the initial flat. In contrast to most well-known models is the relation between the twist angle of the rod and measure delenatii not postulated, and is in the process of solving the problem. Determined that the presence of delenatii entails the dispersion of the phase velocity of torsional wave. It is shown that the simultaneous presence of nonlinearity and dispersion leads to the formation of non-sinusoidal standing waves in a beam propagating with constant speed without changing shape.

Keywords: mathematical model, torsional wave, thin-wall bar, warping, twisting vibrations.