Real Problems On Mechanics
Leader: dr Katica Hedrih
Subject of research
Basic Principles of Mechanics Applied to Nonlinear Dynamical Systems, and to Models of
real discrete and continuum systems of disparate physical nature. Nonlinear oscillations of
dynamical systems. Discrete continuum with viscoplastic, hereditary or creep constraints
and models of continuum with different material properties and discontinuities, as a models
of damage and fracture dynamics. Dynamics and stability of discrete continuum models and
continuum models with cracks. Blance lows and symetry in mcehanics (damage and fracture).
Dynamical active materials and Dynamics of biomaterials. Dynamics of coupled rotation
motions and modelling of dynamics and control of active structure.
Description of the work
- 1. Stable programmed processes. Theory of programing and realizations of stable
processes of developing and reliable prognosis and descibing of natural phenomena. Research
will be directed towards developing a mathematical theory based on preprinciples of existence
and invariability, for constructing stable programs of control processes and phenomena.
- 2. Nonlinear deterministic and stochastic processes in dynamics of mechanical systems and
applications. Dynamics and stability of discrete continuum models with hereditary, and creep
fractional order derivative relations constraints, as well as a thermo and piezorheological
constraints. Dynamical material models with coupled fields. Dynamical active materials.
Discrete dynamical models on damage and fracture mechanics. Nonlinear phenomena in discrete
models continuum dynamics and applications. Nonlinear oscillations and chaos in systems
with coupled continual and discrete dynamical subsystems. Analogy and phenomenological mapping
on system dynamics of disparate nature.
- 3. Research of material with cracks, and composite and new materials. Some problems
of designing, contructing and verifying the reliability and durabnility of mechanical
structures and new materials. Models of rotors with cracks. Problems of mechanical
protectionsof the cuting tools. Molecular design of monolith and composite materials.
- 4. Dynamics modelling and active structure control. Applications of active structures
and industrial robots. Dynamical simullations in nonstationary fields and control of processes.
- 5. New models of the simmulation. Invariant approch to the foundation of shell theory.
Application of invariant approximation in FEM.
- 6. Stability of one and multyciclic resonant oscilations.
- 7. Current problems of biomechanics. Research is directed towards obtaining knowledge
on mechanical injuries of spinal chord and head.
- 8. Blance lows and symetry in mcehanics (damage and fracture).
Originality of research
Nonlinear phenomena in dynamical systems. New discrete continuum models with constraints
of disparate nature, models of dynamical active materials and structures. Mech. injuries
of spinal and head.
Advan. of: mathematical theory of stable programed processes; prognosis and mathematical
description of system nonlinear dynamics; knowledge on nonlinear dynamics and stability of
dynamical systems. Designing, contructing and verifying new discrete models of continuums
with hereditary or creep, fractional order derivative constitutive relations, or thermo
and piezorheological constraints, as dynamicly active materials. Analogy and phenomenological
mapping on system dynamics of disparate nature.
State of the Art in Scientific Field
At the leading intern. Congr. in the area of mechanics, first keywords of plenary and
introducing lectures, of headlines of leading scinetific journals and monographies as
well as of various papers of international significance are: Nonlinear dynamics and chaos,
Analytical dynamics, Nonlinear sciences, nonlinear phenomena, Deterministic Chaos,
Control oscilations, Systems self-similar to the living creatur, dynamics and control
of active structure, damage structure dynamics, computer methods, risk....
The selection of seveeral recent intern. congr. itself, as:
- ICNM-III Third Inter. Confer. on Nonlinear Mechanics, 1998, Shanghai, and new in 2002.;
- IUTAM Symp. "Nonlinearity and Chaos in Engineering Dynamics, London 1993;
- ICIAM Hamburg 1995, ICIAM 99, Edinburg, Third Intern. Congr. Ind. and Applied Methematics;
- 2th Intern. Confer. of Ukrainian Mech.l Engineers, Lviv, 1995; 1997, 1999, 2001.
- IIIrd Euromech Nonlinear Dynamics Confer. Paris, 1999. EUROMECH ENOC Copenhagen 1999.
- GAMM: Hanover 1991, Lajpzig 1992, Drezden 1993, 1994 i 1995, Metz 1999;
- Second Inter.Confer. Control Oscillations and Chaos COC 2000, Saint-Petersburg, Russia.
- Second Intern. Confer. Stability and Control for Transforming Nonlinear
Systems Moscow 2000, provides reference contents for evaluating the concurrent research in the area of mechanics.
References for evaluting the state of research in the area of nonlinear mechanics in our
country are the research results presented at the leading subproject 04M03A Actual Problems
on Mechanics with Appl., the report on which was accepted by the M ST of the R. of Serbia,
as well as papers publsihed in two Yug. Intern. Journ. the area of mechanics Mechanics,
Automatic Control and Robotics (last issue from 2001.) Facta Universiatatis Univer.
of Niš and Theoretical and Applied Mechanics JDM (last issue from 1999.), as well as
two (recently held) Yug. congresses on mechanics with inern. participations: (Niš, 1995
i Vrnj. Banja 1997) and inter. symposia: Yug. Conf. on Nonlinear Deterministic and
Stochastic Processes in Dynamical Systems with Appl. - YCNP NIŠ'91, i Yug. Conf. on
Nonlinear Mechanics-Nonlinear Sciences at the Threshold of the Third Millenium Niš 2000.,
as a Recent Adv. in Analytical Dynamic-Control, Stability and Diff. Geometry, 2001 Belgr.
we can conclude abaot St. of Art.
Planned Project Results
- Results of this research, presented in monographies or in new university textbooks can be
applied in advancement of mechanics programm and in higher education, as well as in practice
of engineers where nonlinear mechanics is applicable.
- Models of rotors with cracks, kinematics and dynamics modelling and active structure
control and their application to active structures and industiral robots as well as the
findnigs about nonlinear processes in dynamics of rotors with multiple rotation axes
allows for reliable calculations fo rotor bearing loads, rotor dynamics and of other
paramters of rotational motion of maschines and structures and optimization and
simplification of their design.
- Findings of dynamics of system s with hereditary elements can be applied in designing
and construucting of engineering systems, as well as in examining and predicting of stability,
reliability and durability of construcction structures with properties of viscoelasticity,
hereditarity retardation and/or relaxation as well as predicting the accuracy of maschine work.
- Findings in th area of damage and fracture mechanics can be used in examining and
evalutaing the reliability and durability of engineering constructions, maschines and
systems, and od various gadgets in civil and mechanical engineering.
- Findings in thre area of nonlinear dynamics which can be presented by a monography
create a theoetical basis for designing of technologies and products based on nonlinear
dynamics, processes and phenomena and their control and based on the separation of fast
and slow oscillations or superpositioning of certain dynamics which give basis foe
designing of a series of products of vibrational maschines for agriculture, mining,
civil engineering and process technologies.
- Construction of active structure and active dynamical materials which can be
controlled is of interest for the creation of new dynamically active materials for
which the military industry should beinterested.
Models of rotors with cracks, kinematics and dynamics modelling and control of active
structures applied to active contrcutions and industrial robots....
It can be used in designing, contructing and examining the durability of rotoexcavators,
reductors, balancing maschines, and for fintuning of gyrorotors and gyrostats.
Obtaining knowledge on mechanical injuries of spinal chord and head. Findings on spinal
chord and head fracture mechanics can be significant for diagnosis of injuries of
spinal chord (spine)....
Molecular design of monolith and composite materials.