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 MAJ 2007.

Pozivamo Vas da učestvujete u radu sednica Odeljenja i to:

CETVRTAK, 10. maj 2007. u 18 sati:


Jan Vondrak, Astronomical Institute, Academy of Sciences of the Czech Republic, Prague
MODERN SPACE OBSERVATIONS OF EARTH ORIENTATION PARAMETERS AND THEIR EXCITATION BY GEOPHYSICAL FLUIDS

The motion of Earth's spin axis in space has been monitored for more than 25 years by VLBI, and since 1994 also its rate has been measured by GPS. The method of "combined smoothing", developed recently at the Astronomical Institute in Prague enables to combine both series. The analysis of the combined solution revealed statistically significant deviations from the model. These differences can be identified with the retrograde Free Core Nutation (FCN) and several forced nutation terms. From the direct analysis of celestial pole offsets follows that the period of FCN apparently grew from original 435 days to 460 days during the past ten years. A study of indirect determination of FCN period, based on the observed nutation terms through the resonance effects however shows that this period is in fact close to 430 days and very stable. We also found that a small additional excitation by geophysical fluids (atmosphere, ocean) should exist, near the FCN frequency, to account for the observed celestial pole offsets in this frequency range.

In order to estimate how well the observed geophysical excitation agrees with the celestial pole offsets, we use an alternative 'integration' approach. We integrate numerically Brzezinski's broad-band Liouville equations in celestial reference frame, using appropriately chosen initial conditions. Only the long-periodic part of geophysical excitation (in celestial frame) is used, and external torques exerted by the Moon, Sun and planets are neglected. The results are then compared with the observed celestial pole offsets measured by VLBI with respect to the IAU2000 model of precession-nutation.

It is demonstrated that these small excitations are capable, thanks to a large amplification due to the resonance, to excite the Earth's nutation significantly. The amplitudes of the excited motion are comparable to the celestial pole offsets observed by VLBI. Both amplitudes and phases of individual nutation terms are sensitive to parameters characterizing the internal structure of the Earth. Among these, the flattening of the outer fluid core is dominant since it gives rise to large resonance effects. All nutation terms are affected, but the most sensitive ones are those with periods close to the period of FCN which, in turn, heavily depends on the dynamical flattening of the core. The nutation terms observed by VLBI, with atmospheric and oceanic excitations removed, can thus serve to determine the flattening, and also the quality factor Q of the Earth at the FCN frequency.

(Profesor Vondrak ce odrzati jos jedno predavanje pod naslovom "An improved astrometric catalogue EOC-3 -step towards a better reference frame for long-term Earth orientation studies"u ponedeljak, 14.05.2007. u 13h, Biblioteka Astronomske opservatorije u Beogradu (ul.Volgina 7).)



SREDA, 16. maj 2007. u 18 sati:


Katica (Stevanovic') Hedrih, Ma~Zinski fakultet, Ni~Z
Novi prikazi klasic(ne dinamike rotora (ili Novi pogled u Kinetiku rotora)

Daju se novi prilozi klasic(nim poglavljima Kinetike rotora. U okviru klasic(ne univerzitetske nastave Dinamike na tehnic(kim i drugim fakultetima izla~^u se poglavlja pod nazivom ~R~Rgeometrija masa~R~R, ~R~Rkinetic(ki pritisci~R~R, ~R~Rreaktivni udar u le~^i~Ztima vratila rotora~R~R. Predavac( je uveo nove vektore momenata inercije masa za pol i osu, materijalnih sistema i prve rezultate publikovao u me?unarodnim c(asopisima Facta Universitatis, ZAMM i Tensor, kao i publikaciji ~R~RThree topics in Mathematics and Mechanics~R~R Matematic(kog instituta 1998, a ove godine izvodec'i nastavu predmeta Dinamika za studente Ma~Zinskog fakulteta dao nove doprinose i potvrde korisne primene, tako uvedenih vektora momenata inercije masa i dao oc(igledne primere da se upotrebom istih mo~^e studentima oc(iglednije, i u krac'em vremenu objasniti pojmovi rotaciono-inercionih svojstava sistema materijalnih tac(aka, stanje momenata inercije masa sistema u odnosu na pol, svojstva rotacionih dinamika materijalnih sistema i tela, kao i dinamika udara sistema, koji dozvoljavaju pojavu rotacija i na kraju balansiranje rotora. Na WEB sajtu www.hm.co.yu/mehanika se nalaze kompletna predavanja iz Kinetike (Dinamike), koja sadr~^e te nove rezultate istra~^ivanja predavac(a unete u nastavu Mehanike.



SREDA, 23. maj 2007. u 18 sati:


Ratko Pavlovic', Ma~Zinski fakultet Ni~Z
Almost sure Stability of a moving elastic Band

In this paper the stochastic stability problem of a moving elastic band subjected to action in-plane acting forces is investigated. Each force consists of a constant part and a time-dependent zero mean stochastic function. By using the direct Liapunov functional method almost sure asymptotic stability conditions are obtained as the function of stochastic process variance, damping coefficient, and geometric and physical parameters of the band. Numerical calculations are performed for infinite mode and compared with known results. Almost sure stability regions are shown for infinite and first mode when is known two-dimensional density probability function, and for higher modes when is edge load Gaussian or harmonic process. Keywords: Random loading, Liapunov functional, Almost sure stability, Gaussian and harmonic proces.

SREDA, 30. maj 2007. u 18 sati:


Aleksandar M. Spasic', Institut za tehnologiju nuklearnih i drugih mineralnih sirovina, Beograd
Teorija elektroviskoelastic(nosti

Primenjen je novi pristup rasvetljavanju fenomena prenosa kolic(ine kretanja i elektrona na rigidnim i deformabilnim me?upovr~Zinama u finim (mikro, nano, ato) disperznim sistemima. Elektroviskoelastic(no pona~Zanje, na primer tec(no-tec(nih me?upovr~Zina (emulzije, dvostruke emulzije), se zasniva na tri oblika ~Snestabilnosti~S, rigidan, elastic(an i plastic(an. Doga?aji podrazumevaju interakcije izme?u unutra~Znjih (imanentnih) i spolja~Znjih (incidentnih) periodic(nih fizic(kih polja. Kako se doga?aji na me?upovr~Zinama finih disperznih sistema posmatraju na nivoima molekula, atoma i/ili entiteta za njihovo razumevanje je neophodno uvesti i fenomen prenosa elektrona pored vec' klasic(no kori~Zc'enih fenomena prenosa u hemijskom in~^enjerstvu, kolic(ine kretanja, toplote i mase. Dakle, entitet se mo~^e definisati kao najmanji nedeljivi element materije vezan za odre?eni fenomen prenosa (diferencijalni element mase/demon, jon, fonon kao kvant akustic(ne energije, infon kao kvant informacije, foton i electron). Za ovako definisani fizic(ki formalizam, teoriju elektroviskoelastic(nosti, razvijena su i diskutovana tri matematic(ka formalizma. Prvi je model tenzora napona, u kome se normalne i tangencijalne sile, samo u matematic(kom smislu, posmatraju bez obzira na njihovo poreklo (mehanic(ko i/ili elektric(no). Drugi model predstavljaju klasic(ne linearizovane homogene i nehomogehne integro-diferencijalne jednac(ina tipa ~SVan der Pol~T. Na kraju, trec'i model predstavlja poku~Zaj generalizacije, linearnih i nelinearnih, homogenih i nehomogenih diferencijalnih jednac(ina tipa ~SVan der Pol~T, zamenom izvoda i integrala celobrojnog reda odgovarajuc'im izvodima i integralima necelobrojnog reda (p = n ~V ?, n = 1, 2).

Sednice se održavaju u zgradi SANU, Knez Mihailova 35, u sali 2 na prvom spratu.

Sekretar Odeljenja
Bojan Međo
Upravnik Odeljenja
Akademik Teodor Atanacković, s.r.