On the spectra of composite materials with different dissipation models

Abstract

The article deals with the issues of qualitative behavior and methods for calculating the spectra of natural vibrations of a layered composite consisting of elastic and viscoelastic phases with dissipation. As a viscoelastic phase, it is proposed to consider a viscoelastic material with exponential aftereffect kernels, with aftereffect kernels in the form of Rabotnov functions, a material with Kelvin-Voigt friction and a material with fractional Kelvin-Voigt friction. A general scheme is given for studying the qualitative properties of the spectra of one-dimensional oscillations and a method for calculating one-dimensional oscillations, which consists in reducing the spectral problem to solving algebraic equations. The question of the convergence of natural frequencies of oscillations of composite samples to the natural frequencies of averaged boundary value problems, which are non-self-adjoint, is discussed.