Seminar za računarstvo i primenjenu matematiku, 26. februar 2019.

• 25. Februar,  2019
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Naredni sastanak Seminara biće održan u utorak, 26. februara 2019. u sali 301f Matematičkog instituta SANU sa početkom u 14:15.

Predavač: Katica R. (Stevanović) Hedrih, Department of Mechanics, Mathematical Institute of Serbian Academy of Science and Arts, Belgrade, Serbia

Naslov predavanja: FRACTIONAL TYPE MODES OF THE VIBRATIONS OF DISCRETE CONTINUUM HYBRID SYSTEMS CONTAINING MULTI-DEFORMABLE BODIES

Apstrakt: In this lecture, on the basis of the series of the author`s previous published results of the analytical dynamics and vibrations of the fractional type discrete, as well as discrete continuum hybrid systems, an analysis about independent fractional type modes of free and forced vibrations of the hybrid systems of fractional type with multi-deformable bodies is performed. A hybrid discrete continuum system of fractional type with multi-deformable bodies consists of ideal elastic bodies (belts, beams, membranes, plates) with same boundary conditions, coupled by standard light fractional type discrete continuum layers in transversal direction permitting the system transversal vibrations.  Independent fractional type modes appear in each of eigen time function of each of the eigen amplitude modes in regimes of the free, as well as in regimes of the forced transversal vibrations of discrete continuous system. Number of the independent fractional type modes in each of the eigen time function of each of the eigen amplitude modes is equal to number of the coupled deformable bodies in hybrid fractional type system.  Main new result presented in this paper is description of the forced fractional order vibration with corresponding analytical approximate solution for forced vibrations expressed by integral of the convolution and using Laplace transformation. Use this result, independent fractional order modes of each of the eigen time functions in each of the eigen amplitude function form the set of infinite number of eigen amplitude functions, are defined with two characteristic numbers and corresponding number of external excitation forced frequencies.

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