MECHANICS OF MACHINES AND MECHANISMS - MODELS AND MATHEMATICAL METHODS
Plan rada Seminara Mehanika mašina i mehanizama - modeli i matematičke metode za NOVEMBAR 2022.
UTORAK, 01.11.2022. u 17:00, sala 301f, Kneza Mihaila 36 i Live stream
Nikola Mirkov, “Vinča” Institute of Nuclear Sciences – National Institute of the Republic of Serbia, University of Belrgade, Serbia
COMPUTATIONAL MECHANICS – SHOULD WE CODE IT OURSELVES?
Using computational tools is ubiquitous in research in mechanics these days. However, there are still some challenges that have been pointed out, and these have a lot in common with all of computational science in general. These are the issues of reproducibility. As some have formulated it, there are needless roadblocks in the path of reproducibility in computational science and engineering. If that is the assertion what are the approaches, we ask, that can alleviate the problems? In this exposition we would like to discuss these and some of the related matters while talking about personal experience in the development of the free and open-source computational library for continuum mechanics. What is the role of writing your own software in the current (conditionally termed) crisis of reproducibility? Is the coding the thing of the past since we have very developed commercial solutions, or the time is ripe for different approach having new generations that talk in code and in large numbers look for jobs in software industry? What is the unit of discourse for a researcher in computational science and engineering? These some of the questions. Let us have an open discussion.
UTORAK, 15.11.2022. u 17:00, sala 301f, Kneza Mihaila 36 i Live stream
Simona Doneva, Department of Applied Mechanics, Lublin University of Technology, Lublin, Poland; Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria
Jerzy Warminski, Department of Applied Mechanics, Lublin University of Technology, Lublin, Poland
Emil Manoach, Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria
NONLINEAR THERMO-ELASTIC VIBRATIONS OF PLATES AND BEAMS
In the present work a large amplitude thermo-elastic vibrations of a circular plate and a nonlinear dynamic behavior of a bi-material beam is analyzed.
Geometrically nonlinear thermo-elastic vibration of a Mindlin circular plate is studied by two different methods. In the first approach-FEM is demonstrated that the elevated temperature can change dramatically the response of the plate and could provoke the plate to complex response, including buckling and bifurcations. The second approach allows to obtain easily the resonance curves and to study the influence of the loading parameters and elevated temperature on the behavior of the plate.
The bi-material thermo-elastic beam model is based on geometrically nonlinear version of the Timoshenko beam theory. The extended equations of motions of vibrating beams at elevated temperature are studied analytically by the harmonic balance method and resonance curves for different parameters of the mechanical and thermal loading are obtained. The coupled vibrations of the beam are studied by using 3D finite element analysis.
SREDA, 16.11.2022. u 16:15, sala 301f, Kneza Mihaila 36 i Live stream
Emil Manoach, Institute of Mechanics-Bulgarian Academy of Sciences, Bulgaria
VIBRATIONAL METHODS FOR STRUCTURAL HEALTH MONITORING AND DAMAGE DETECTION OF STRUCTURES
The lecture is devoted to the problems in structural health monitoring (SHM) and damage detection (DD). The main goals and main stages of DD of structures are formulated. The most of the popular modal based methods for DD are presented: modal shapes, modal slopes, modal curvatures, modal strain energy methods, modal damping. Then the forced response methods are considered and some new methods based on the forced response of the structures are explained. Special attention is paid for the Poincaré map based method, the improved Poincaré map based method, Selective index method, and Shear force method. All presented methods are numerically validated and some of them are tested experimentally by using high speed camera and a scanning laser vibrometer.
The advantages of the offered methods and their application in SHM are demonstrated by numerical simulations and experimental tests.
Zajednički sastanak sa Odeljenjem za Mehaniku
SREDA, 16.11.2022. u 18:00, sala 301f, Kneza Mihaila 36 i Live stream
Svetoslav G. Nikolov, Institute of Mechanics-Bulgarian Academy of Sciences, Bulgaria
NONLINEAR DYNAMICS OF MECHANICAL AND BIOMECHANICAL SYSTEMS – ANALYTICAL AND NUMERICAL INVESTIGATION
It is well-known that autonomous nonlinear differential system of the form $dx/dt=f(x,\lambda)$, $x\inR^n$, where $n\ge 3$ and $\lambda$ is the vector of parameters, can display a rich diversity of periodic, multiple periodic, chaotic and hyper-chaotic flows dependent upon the specific values of one or more bifurcation (control) parameters. A principal problem toward complete understanding of nonlinear interactions is to identify where in its phase space one dynamical system is structurally stable. For example, in a small neighborhood of a structurally stable Poincare homoclinic orbit lie only periodic orbits from saddle type. On the contrary, near a structurally unstable homoclinic orbit may exist both structurally unstable and attractive periodic orbits in addition to saddle ones. Note that after Smale’s works these systems are said to be Morse-Smale systems. The structural stability (roughness) investigation of steady state and of limit cycles or other types of trajectories is a main problem in bifurcation theory. It is well-known that there is critical dependence of the stability conditions of limit cycles on the stability conditions of its steady states. Based on classical works in the literature, it was defined that by knowing the sign of Lyapunov values (called also focus values, Lyapunov quantities (coefficients)) we can efficiently study the structure of complicated nonlinear system trajectories. In other words, the type of: 1) stability loss of equilibrium and 2) winding/unwinding of system trajectories in small neighbourhoods of equilibrium depend on the sign of Lyapunov value. In this presentation, we focus our attention on the investigation of the nonlinear behavior of different mechanical and biomechanical systems.
Zajednički sastanak sa Odeljenjem za Mehaniku
UTORAK, 29.11.2022. u 17:00, sala 301f, Kneza Mihaila 36 i Live stream
Stepa Paunović, Matematički institut SANU, Beograd, Srbija
DINAMIKA SISTEMA POVEZANIH FRAKCIONO PRIGUŠENIH GREDA SA PIJEZOELEKTRIČNIM SVOJSTVIMA
U okviru ovog predavanja biće izložen mehanički i matematički model sistema povezanih greda čije se prigušenje modelira uz primenu Kelvin-Vojtovog (Kelvin - Voigt) modela prigušenja sa izvodima necelog reda, pri čemu bilo koji broj greda sistema može biti bimorfan, odnosno imati pridodate pijezoelektrične elemente. Nakon izvođenja i rešavanja jednačina sistema, biće prikazan i postupak projektovanja ovakvih mehanizama, odnosno prilagođavanje njegovih dinamičkih karakteristika specifičnim potrebama. Na kraju će biti izložen i koncept korišćenja periodičnog sistema povezanih greda i dinamičkih fenomena koji se kod njega javljaju, za kontrolu prostiranja mehaničkih talasa kroz sistem i prevođenje dela mehaničke energije talasa u električnu energiju, kao i mogući pravci unapređenja i daljeg razvoja ovog postupka.
Obavezno je nošenje maski i održavanje distance. Broj prisutnih na predavanju ograničen na najviše 10 (uključujući i predavača).
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.
dr Ivana Atanasovska