Project 1616

Real Problems On Mechanics

Leader: dr Katica Hedrih

Abstract

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.

Research Goal

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

World-wide Situation

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.

Domestic Situation

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.