Plan rada Seminara iz Biomehanike, bioinžinjeringa i matematičke biologije za NOVEMBAR 2023.
Četvrtak, 30.11.2023. u 13:00, regionalni centar Niš, Pariske Komune bb, Niš
Katica R. (Stevanović) Hedrih, Serbian Scientific Society, Mathematical Institute of Serbian Academy of Sciences and Arts, Belgrade, Serbia; Faculty of Mechanical Engineering, The University of Niš, Niš, Serbia
DIFFERENTIAL OPERATOR OF FRACTIONAL ORDER - AN ELEMENT OF MATHEMATICAL PHENOMENOLOGY IN THE ANALOGY OF MODELS, FRACTIONAL TYPE, TORSIONAL OSCILLATIONS OF SHAFTS AND TREES
The differential operator of fractional order is used to model two mathematically analogous oscillatory models of fractional type, one mechanical and the other biodynamical. Using the differential operator of fractional order, the constitutive relation of the material of the shaft and the analogous constitutive relation of the tree trunk are compiled. A system of three fractional-order ordinary differential equations of torsional eigen and forced oscillation modes of shafts with three disks was written. It was shown that the same system of those three fractional-order ordinary differential equations describes the torsional oscillations of a tree with three with two-branches modeled by discrete fractal sets. Approximate analytical expressions of natural and forced torsional oscillatory modes, of the fractional type, were determined using Laplace transformation, power series and convolution integrals. Graphic representations of natural and forced modes of the fractional type are given, in the form of surfaces and for the exponent of the fractional order of differentiation in the interval from zero to one. Part of the results was published in the paper: K. R. (Stevanovi ́c) Hedrih Andjelka N. Hedrih: The Kelvin–Voigt visco-elastic model involving a fractional-order time derivative for modelling torsional oscillations of a complex discrete biodynamical system, Acta Mechanica, (2022), Doi: 10.1007/s00707-022-03461-7, while part of the results is presented to the public by the lecturer for the first time. All results were achieved in co-authorship with dr. Andjelka Hedrih, who is the "spiritus movens" of ideas about biosystem dynamics.
Zajedničko predavanje sa seminarom Odlučivanje-teorija, tehnologije i primena.