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

**Mechanics Colloquim **

** PROGRAM**

MATEMATIČKI INSTITUT SANU

ODELJENJE ZA MEHANIKU

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PROGRAM ZA JULI 2011.
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Pozivamo Vas da učestvujete u radu sednica Odeljenja i to:

__Ponedeljak, 4. juli 2011. u 13 sati:__

Lecture No 1159

* Subhash C. Sinha, Alumni Professor and Director, Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, AL 36849, USA *

** ANALYSIS AND CONTROL OF PARAMETRICALLY EXCITED SYSTEMS: A NEW APPROACH **

Abstract: A general framework for the analysis and control of parametrically excited linear/nonlinear dynamical systems is presented. This class of problems appears in the modeling of rotorcraft blades in forward flight, asymmetric rotor-bearing systems, automotive components such as connecting rods, universal joints, asymmetric satellites, fluids under gravity modulations, etc. These dynamical systems are represented by a set of differential equations which contain time-periodic coefficients. First, an efficient computational scheme for the solution of linear problem is discussed through an application of Chebyshev polynomials. The idea is further developed to obtain the Lyapunov-Floquet (L-F) transformation associated with a linearized or a quasilinear time-periodic dynamical system. An application of L-F transformation yields equivalent systems whose linear parts are time-invariant. Therefore, the controls for all time-periodic linear systems can be designed using the standard time-invariant methods such as pole placement or optimal control theory. A symbolic control technique for Floquet multiplier placement is also suggested for linear time-periodic systems.

In the case of nonlinear systems, a periodic orbit in the original coordinates has a fixed point representation after the L-F transformation. The local stability and bifurcation analyses are studied via time-dependent enter manifold reduction' and ormal form theory'. Results for fold, flip and secondary Hopf bifurcations are discussed. Bifurcation control and feedback linearization techniques for nonlinear time-periodic systems are also developed and applied to some typical problems. Further, the order reduction problem associated with free and forced parametrically excited large-scale nonlinear systems is also addressed using an invariant manifold approach. A methodology for reduced order controller design is also suggested.

The practical significance of these approaches is demonstrated through simulations and experimental investigations of a number of mechanical systems. These include vibration control of a multi-bladed rotor, shafts supported by magnetic bearings, bifurcation analyses of a flexible slider crank mechanism and an autoparametric mechanical system, among others.

__SREDA, 20. juli 2011. u 18 sati:__

Lecture No 1160

* Prof. Peter Bradshaw Professor of Experimental Aerodynamics, Department of Aeronautics, Imperial College, London University. England Dr. Srba Jovic NASA, Kalifornija *

Abstract: The enormous range of length scales makes it impossible to solve the exact Navier-Stokes (N-S) equations directly ("Direct Numerical Simulation" or DNS) for high-Reynolds-number turbulent flows. The most gentle simplification is to solve N-S for large scales and to approximate ("model") the small eddies (Large Eddy Simulation, LES). Near a solid surface, unfortunately, there are NO large eddies! The approximate small-eddy model has to be used for the full range of length scales. This is the big obstacle to using LES in "wall-bounded" flows. Today's engineers use Reynolds-Averaged N-S (RANS) equations. Usually, the complete range of eddy sizes is represented by just one length scale (plus the viscous length scale needed near solid surfaces). Nearly all the terms in the equations are modeled, i.e. replaced by dimensionally-correct and physically plausible combinations of the length and velocity scales and their spatial gradients. Each modeled term contains an empirical parameter, usually a constant. The most obvious way to produce a RANS model is to derive Reynolds-averaged transport equations for all the mean-velocity components and all the Reynolds stresses, and model the unknown terms. This has been done quite successfully, but stress-transport models have the reputation of suffering numerical problems. This reputation dates from 20-30 years ago at least. The ratio of a Reynolds stress to the rate of strain in the plane of that stress defines a so-called "eddy viscosity". It is different for different stresses, and varies greatly in space within the flow domain. It is a physically-meaningful quantity only if the scales of the turbulence are closely related to the scales of the mean flow. Most current engineering prediction methods are based on a scalar eddy viscosity (same for all stresses, a.k.a. isotropic") defined as (

The review will end with a discussion of the capabilities of today's prediction methods.

Predavanja ce se odrzavati sredom sa pocetkom u 18.00 casova, u sali 301 F na trecem spratu zgrade Matematickog instituta SANU, Knez Mihailova 36/III, (zgrada preko puta glavne zgrade SANU).

Poziv naucnicima i istrazivacima da prijave svoja predavanja:

Prijava potencijalnog predavaca treba da sadrzi apstrakt predavanja do jedne stranice na srpskom jeziku cirilicom i prevod na engleski jezik, kao i CV obima do dve stranice. Prijavu poslati na adresu upravnika Odelenja za mehaniku u vidu Word DOC na adresu: khedrih@eunet.rs

Start of each lecture is at each Wednesday at 18,00 h in room 301 F at Mathematical Institute SANU, street Knez Mihailova 36/III.

Announcement and Invitation:

All scientists and researchers in area of Mechanics are invited to contribute to the Program of Mechanics Colloquium of Mathematical Institute of Serbian Academy of Sciences and Arts. One page Abstract of proposed Lecture with short CV is necessary to submit in world doc to Head of Department of Mechanics (address: khedrih@eunet.rs), one month before first day in the next month.

Sekretar Odeljenja

dr Srdjan V. Jovic

sekretar Odelenja za mehaniku

Matematickog instituta SANU, Beograd

e-mail: jovic003@yahoo.com

dr Srdjan V. Jovic

sekretar Odelenja za mehaniku

Matematickog instituta SANU, Beograd

e-mail: jovic003@yahoo.com

Upravnik Odeljenja

Prof. Dr. Katica R. (Stevanovic) Hedrih

Prof. Dr. Katica R. (Stevanovic) Hedrih