Mechanics Colloquim
PROGRAM
PROGRAM ZA JULI 2011.
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
A Review of Turbulent Flow
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 (
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).
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.
The review will end with a discussion of the capabilities of today's prediction methods.
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
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.
dr Srdjan V. Jovic
sekretar Odelenja za mehaniku
Matematickog instituta SANU, Beograd
e-mail: jovic003@yahoo.com
Prof. Dr. Katica R. (Stevanovic) Hedrih