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ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

Mechanics Colloquim

PROGRAM

MATEMATIČKI INSTITUT SANU
ODELJENJE ZA MEHANIKU

PROGRAM ZA MART 2014.

Pozivamo Vas da učestvujete u radu sednica Odeljenja i to:

Sreda, 5. mart 2014. u 18 casova, sala 301f:
Katica (Stevanovic) Hedrih, (Project Leader in Mechanics and Head of Project ON174001 by 24 chapter of AKT of MPNTR PS, Mathematical Institute SANU) :
ELEMENTS OF MATHEMATICAL PHENOMENOLOGY IN DYNAMICS OF MULTI-BODY SYSTEM WITH FRACTIONAL ORDER DISCRETE CONTINUUM LAYERS

Dynamics of multi deformable, ideal linear elastic bodies (beams. plates, membranes, belts with corresponding same boundary conditions) coupled by standard light fractional order discrete continuum layers is considered by using Petrovic.s theory of elements of mathematical phenomenology. The sixth chapter of Petrovic.s theory contain phenomenological analogies, including the mathematical analogies and qualitative analogy. Starting with coupled fractional order differential equations along transversal displacements of the linear elastic beams, same boundary conditions, and coupled by fractional order discrete continuum layers, system of coupled ordinary fractional order differential equations along eigen time functions in which eigen amplitude functions is obtained. Independent eigen main fractional order modes and set of characteristic numbers of the corresponding eigen time functions corresponding to eigen amplitude function are obtained. Using Petrovic's theory of mathematical analogy and qualitative analogy properties of eigen main fractional order modes and characteristic numbers of time functions of vibrations of multi-plates as well as multi-membranes coupled by fractional order discrete continuum layer are obtained. A energy analysis is presented and fractional order dissipation of system energy defined. By phenomenological mapping between the eigen main fractional modes of eigen time functions in one eigen amplitude form and eigen main fractional order modes of a fractional order chain dynamics and of a fractional order electrical chain are identified qualitative and mathematical analogies. Keywords: Multi deformable body system, fractional order discrete continuum layer, partial fractional order differential equations, fractional order modes, characteristic numbers, phenomenological mapping, qualitative analogy, mathematical analogy, mechanical chain, electrical chain.

References:

[1] Petrovic, M., Fenomenolosko preslikavanje (Phenomenological mapp), Srpska kraljevska akademija, Beograd, 1933. str. 33.

[2] Petrovic, M., Elementi matematicke fenomenologije (Elements of mathematical phenomenology), Srpska kraljevska akademija, Beograd, 1911. str. 789.
http://elibrary.matf.bg.ac.rs/handle/123456789/476?locale-attribute=sr

[3] Katica R. (Stevanovic) Hedrih, (2013), Fractional order hybrid system dynamics, PAMM, Proc. Appl. Math. Mech. 13, 25 . 26 (2013) / DOI 10.1002/pamm.201310008.

[4] Hedrih (Stevanovic) K., (2013), Two mass particle fractional order plane system dynamics, Dynamical Systems . Theory, Edited by JAN AWREJCEWICZ, MAREK KAMIERCZAK, PAWE OLEJNIK, JERZY MROZOWSKI, 2013, pp. 403-4012. . ISBN 978-83-7283-588-8, Printed by: Wydawnictwo Politechniki zkiej, www.wydawnictwa.p.lodz.pl.

[5] Hedrih (Stevanovic) K., (2013), A generalization of Lagrange method of variation constants, SCIENTIFIC REVIEW, Special Issue Nonlinear Dynamics, Dedicated to Milutin Milankovic (1879- 1958), Guest Editors: Katica R. (Stevanovic) Hedrih and Zarko Mijajlovi S2 (2013) pp. 37-66, Serbian Scientific Socienty, YU ISSN 0350-2910
http://afrodita.rcub.bg.ac.rs/~nds/
http://afrodita.rcub.bg.ac.rs/~nds/indexe.html

[6] Hedrih (Stevanovic) K., (2008), The fractional order hybrid system vibrations, Monograph, Chap in Monograph. Advances in Nonlinear Sciences, ANN, 2008, Vol. 2, pp. 226-326.

[7] Hedrih (Stevanovic) K., (2011), Analytical mechanics of fractional order discrete system vibrations. Chap in Monograph. Advances in nonlinear sciences, V... 3, JANN, Belgrade, pp. 101-148, 2011. ISSN: 978-86-905633-3-3.

[8] Hedrih (Stevanovic) K., (213), Fractional order differential equations of dynamics of two mass particles, constrained by a fractional order element, Plenary Lecture, Two pages Extended abstract, 8th INTERNATIONAL SYMPOSIUM ON CLASSICAL AND CELESTIAL MECHANICS (CCMECH.8), September 25 . 29, 2013, Siedlce, Poland, ( The Russian Academy of Sciences, A. A. Dorodnicyn Computing Centre of RAS, Moscow State University, Moscow State Aviation Institute, Warsaw University of Life Sciences, and Collegium Mazovia in Siedlce (Poland) will hold the Eighth International Symposium on Classical and Celestial Mechanics (CCMECH.2013) at Collegium Mazovia in Siedlce, Poland) Book of Abstracts, pp. 27-28. ISBN 078-83-63169-4, @Copyright by Collegium Mazovia.
http://agora.guru.ru/display.php?conf=CCMECH7, http://www.msz.gov.pl/en

[9] Hedrih (Stevanovic) K., (2013), Generalized function of fractional order dissipation of system energy and extended Lagrange differential equation in matrix form, Dedicated to 86th Anniversary of Radu MIRON.S Birth. 30 minutes Plenary Lecture, Abstracts of THE 13th INTERNATIONAL CONFERENCE OF TENSOR SOCIETY ON DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, AND INFORMATICS BESIDES., The 86th Anniversary of Radu MIRON.S Birth. September 3rd (Tuesday) to September 7th (Saturday) in 2013. Faculty of Mathematics, Alexandru Ioan Cuza University and Mathematical Institute .O.Mayer. in Iai Romania And Tensor Society, Japan, 2013, p.3. (paper submitted for publishing in the journal Tensor of Tensor Society, Japan.).
http://www.math.uaic.ro/~tensorconference2013/.

Petak, 21. mart 2014. u 14 casova, sala 301f:

PREDSTAVLJANJE PROJEKATA KOJI SE BAVE MEHANIKOM

Predavanja su namenjena sirokom krugu slusalaca, ukljucujuci studente redovnih i doktorskih studija. Odrzavaju se sredom sa pocetkom u 18 casova u sali 301f na trecem spratu zgrade Matematickog instituta SANU, Knez Mihailova 36.

dr Katarina Kukic
Sekretar Odeljenja za mehaniku
Matematickog instituta SANU
dr Vladimir Dragovic
Upravnik odeljenja za mehaniku
Matematickog instituta SANU

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