Seminar
MECHANICS OF MACHINES AND MECHANISMS - MODELS AND MATHEMATICAL METHODS

 

PROGRAM

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Plan rada Seminara Mehanika mašina i mehanizama - modeli i matematičke metode za DECEMBAR 2018.

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UTORAK, 04.12.2018. u 17:00, Sala 301f, MI SANU, Kneza Mihaila 36
Danilo Karličić, Mathematical Institute of SASA, Belgrade, Serbia
DYNAMIC STABILITY OF NONLOCAL BEAMS AND PLATES
In general, dynamic stability analysis of structures elements such as beam, plate and shells can play a significant role in design procedures of future mechanical and civil structures. For example, in axially loaded beams, where loads are time-dependent harmonic functions, a failure may occur due to dynamic instability might be much smaller than the failure induced by static buckling. These instability conditions usually lead to the failure of micro devices or macro engneering structures. Based on that fact, in this presentation we will show how to analyse stability regions caused by primary parametric resonance, where the frequency of excitation is two times larger than the first natural frequencies of beam/plate in framework of nonlocal elasticity theory. By considering the Euler–Bernoulli beam theory, nonlocal constitutive relation and von Karman nonlinear strains, we obtain a system of nonlinear partial differential equations of motion. Single-mode Galerkin discretization will be employed to obtain a system of m nonlinear differential equations that will be solved using the IHB method in order to obtain semi-analytical periodic solutions of the nonlinear system. Moreover, the stability of periodic solutions will be examined by introducing the Floquet theory. In the second part of this presentation we will discuss about stochastic stability of nonlocal beams and plates in linear regimes. By introducing the perturbation method and definition of the stochastic stability such as the moment Lyapunov exponent, we will show how the approximate analytical solution of the p-th moment Lyapunov exponent is obtained. In addition, we use results for the p-th moment Lyapunov exponent to analyse the moment and almost-sure stability boundaries of a presented stochastic dynamical systems. At the end of the presentation we will show influence of small-scale on the on the dynamical behaviour of the presented models.

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UTORAK, 11.12.2018. u 17:00, Sala 301f, MI SANU, Kneza Mihaila 36
Gordana Kastratović, Faculty of Transport and Traffic Engineering, University of Belgrade, Serbia
NUMERICAL COMPUTATION OF STRESS INTENSITY FACTORS OF SUPPORTING AERO STRUCTURES WITH MULTIPLE SITE DAMAGE
Multiple site damage (MSD) represents the simultaneous development of fatigue cracks at multiple sites in the same structural element. It often occurs in longitudinal and circumferential riveted lap joints in wings and fuselages, and can be very serious, because of possible link up of adjacent cracks creating one large crack that can cause catastrophic failure. The prediction of crack-growth rate, residual strength and fatigue life in the presence of MSD, requires accurate calculation of the Stress Intensity Factors (SIFs) at each crack tip. The problem becomes more difficult when crack propagation has to be treated and therefore successive calculations are required. As technology and computer sciences became more available, numerical computational methods had become an indispensable tool for SIFs determination, but they remain a challenging problem in computational fracture mechanics. This presentation embodies an effort to explore and to demonstrate the capacity, performances and difficulties of SIFs determination by usage of some widely available numerical computational methods. The stress intensity factors for several aero structural configurations with MSD were considered by using three different computational methods: finite element method (FEM) with singularity elements, extended finite element method (X-FEM), and the approximate method based on superposition. This talk represents a review of investigations carried out in cooperation with A. Grbovic, N. Vidanovic and A. Sedmak.
Predavanje se odlaže zbog bolesti predavača. Novi termin će biti naknadno utvrđen i objavljen.

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UTORAK, 18.12.2018. u 17:00, Sala 301f, MI SANU, Kneza Mihaila 36
Katica (Stevanović) Hedrih, Mathematical Institute of SASA, Belgrade, Serbia
PRESENTATION OF THE RESEARCH RESULTS: PROJECT 174001 (2011-2018) DYNAMICS OF HYBRID SYSTEMS WITH COMPLEX STRUCTURES. MECHANICS OF MATERIALS
The project has produced original scientific results in the following themes:

1. Elements of mathematical phenomenology and applications (in Mechanics, in nonlinear dynamics in general, in integration of scientific knowledge in reduction of number of models of dynamical systems).
2. Analytical mechanics of discrete fractional order systems; Derived a series of theorems.
3. Nonlinear and rare phenomena in dynamics of hybrid systems with coupled structures of rigid and deformable bodies; Transfer of energy through a system and subsystems; Synchronization of subsystems.
4. Models of biodynamical oscillators; Phenomenon of transfer of signals, information and energy through their complex structures; Oscillations of DNA helix chains and discrete continuum models of Zone Pelucida, a biomechanical oscillatory model of the mitotic spindle.
5. Mechanics of discrete continuum models. Dynamics of coupled structures of deformable bodies and discrete continuum layers with different constitutive relations: Linear elastic, nonlinear elastic, visco-elastic, hereditary and fractional order properties.
6. Phenomenon of dynamics of systems with friction and vibro-impact system; Theory of collision of rolling bodies; Dynamics of billiards.
7. Mechanics of damage and fracture.
8. Control of systems with delay and theorems of stability.
9. Continuation of doctoral research in accordance with scientific based themes by younger PhD students. 13 PhD students, younger than 30 years of age, are included in the project team and its scientific research. All of them were participants of the two year seminar. So far, 13 PhD students completed all courses at doctoral study programs; 11 candidates defender their doctoral dissertations.

Other topics considered in the framework of the project are: nonlinear transformation, rheonomic system, nonholonomic constraints, mass moment vectors, gyro-rotor dynamics, approximation, amplitude-frequency characteristic, stability, synchronization, theory of collision, vibro-impact system, dynamics of billiards, energy analysis, non-local theory and applications, biomechanical oscillators, control motion. The project collaborators participated in the conferences ENOC 2011, 2014 and 2017, IUTAM ICTAM 2012 and 2017, ESMC 2012 and 2018, EURODYN 2017, Mini-symposium Nonlinear Dynamics 2012, 2014, 2015 and 2017, etc. A member of the project was awarded EuroMech Young scientific prize Roma 2011. Number of Doctoral dissertations defended by members of Project team is 11.
Home page of the Project activities: https://www.mi.sanu.ac.rs/novi_sajt/research/projects/174001a.php.

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Seminar Mehanika mašina i mehanizama - modeli i matematičke metode započeo je sa radom u junu 2018.god. Seminar se održava do dva puta mesečno, utorkom u periodu od 17.00 - 19.00 u Matematičkom institutu SANU.

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