ON PROBLEM OF PROPERTIES OPTIMIZING FOR VISCOELASTIC MATERIALS USING THE BEGLEY-TORVIK EQUATION

Recently, fractional calculus has been the focus of attention of many researchers in the field of science and technology, since a more detailed study of physical processes leads to the need to complicate the mathematical models that describe them, and, consequently, to the study of the behavior of solutions of differential equations containing, along with " ordinary", or "classical", derivative, also fractional. Processes of this kind can include: studies of continuous media with memory, fluid filtration in media with fractal geometry, physical aspects of stochastic transfer and diffusion, mathematical models of a viscoelastic body, models of damped oscillations with fractional damping (for example, vibrations of rocks during earth-quakes or vibrations nanoscale sensors), models of non-local physical processes and phenomena of a fractal nature; climate models, etc. The paper studies boundary value problems for the equation of motion of an oscillator with viscoelastic damping (the Begley-Torvik equation) in the case when the damping order is greater than zero but less than two. Such problems model many physical processes, in particular, the vibration of a string in a viscous medium, the change in the deformation-strength characteristics of polymer concrete under loading, etc. This paper is devoted to optimizing the parametric control of the Begley-Torvik model. A fundamentally new, efficient algorithm is proposed that allows estimating the parameters of a model of real material.