Methods for Optimizing the Deformation-Strength Characteristics of Polymer Concrete

This study investigates boundary value problems for the equation of motion of an oscillator with viscoelastic damping when the damping order is greater than zero but less than two. Such problems model various physical processes, including the oscillation of a string in a viscous medium, changes in the deformation and strength properties of polymer concrete under loading, and others. This work provides a justification for the method of variable separation for the equation of string oscillation with friction in a medium with fractal geometry. In numerous articles on this topic, when using the method of separation of variables, there is often a previously nowhere proven statement about the absence of associated functions in the associated boundary value problems. In this paper, in particular, this important assertion is proved. The Green’s function (influence function) is also investigated, studied problem. It is proved that this Green’s function (influence function) is non-negative, which makes it possible to establish the main oscillatory properties of the problem under consideration.