Abstract
A rod made of a material with a negative Poisson's ratio (auxetic material) is considered. Such materials were first synthesized at the end of the last century and have since been actively studied. In linear and nonlinear formulations, the problem of the propagation of a longitudinal rod wave is considered. It is shown that if for ordinary materials the velocity of longitudinal waves in the rod is greater than the velocity of shear waves and the dispersion is normal, i.e. the value of the phase velocity of the wave exceeds the value of its group velocity, then the qualitatively different (anomalous) behavior of the linear waves is observed in the rods from auxetic materials: there the value of the group velocity in the wide frequency range exceeds the value of the phase velocity. Accounting for geometric and physical elastic nonlinearities, in turn, leads to the possibility of forming in a rod of stationary deformation waves a substantially non-sinusoidal profile - solitons and their periodic analogues. Dependences connecting speeds, wave numbers and amplitudes of nonlinear waves are determined. Keywords: negative Poisson's ratio, kernel, wave, dispersion, nonlinearity.
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