Mechanics Colloquim
PROGRAM
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.