ИСТИНА

The article deals with the problems of constructing effective characteristics of a layered composite material, the layers of which are viscoelastic material. In this case, the hereditary property of viscosity is modeled using the Rabotnov functions, which have singularities at zero. It is proved that the average properties of a material can be analytically described in the form of a homogeneous viscoelastic material with memory, which is also specified using kernels, which are also specified analytically by the Rabotnov functions. It is of interest to study the natural vibrations of such a material. The easiest way is to obtain analytical formulas for the natural frequencies of oscillations transverse with respect to the layers. Such analytical expressions for natural frequencies are obtained in the present work. The spectra are compared for the case of composites made of elastic materials, materials in which nonlocal terms are specified with the help of exponential functions and with the help of Rabotnov functions.