Антиплоские задачи о движении осциллирующей нагрузки по границе упругой изотропной полосы при наличии поверхностных напряжений

Abstract

In this paper, symmetric and antisymmetric antiplane problems about the motion with a constant subsonic velocity of an oscillating load along the boundary of an elastic isotropic nanothin strip are considered. The nanoscale strip thickness is considered by introducing surface stresses in accordance with the Gurtin-Murdoch theory. According to this theory, it is assumed that, in addition to external loads, surface stresses act on the layer boundaries, which are described by Hooke's surface law. As a result, the properties of the elastic material of the strip with nanoscale thickness become different from the material properties of a regular-sized body. A standard technique was used for the so-lution, including the application of limiting absorption principle, the Fourier transform over infinitely extended co-ordinate and the theory of residues for finding the inverse Fourier transform. For various strip thicknesses, solutions were obtained in the form of series in natural waves, dispersion relations were studied, and graphs of the displace-ment amplitudes along the thickness were plotted. The analysis showed that for fixed values of frequency and velocity of the source, the values of non-negative real wave numbers are greater in the presence of surface stresses than the values of the wave numbers for the classical case of the problem without surface stresses. It is noted that surface stresses have a significant effect only when the strip thickness decreases to nanosizes.