MECHANICS OF MACHINES AND MECHANISMS - MODELS AND MATHEMATICAL METHODS
Plan rada Seminara Mehanika mašina i mehanizama - modeli i matematičke metode za APRIL 2019.
UTORAK, 09.04.2019. u 17:00, Sala 301f, MI SANU, Kneza Mihaila 36
Slaviša Šalinić, Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, Serbia
ON THE MODELLING OF FLEXIBLE EULER-BERNOULLI, RAYLEIGH, AND TIMOSHENKO BEAMS BY A NEW LUMPED-PARAMETER DISCRETIZATION THECHNIQUE
A new lumped parameter method for buckling and bending vibration analysis of a flexible beam subject to an axial compressive load with attached springs and lumped masses at the beam ends is presented. The method represents modification of the classical Hencky bar-chain model. Three types of beams are considered: Euler-Bernoulli, Rayleigh, and Timoshenko beams. The method proposed consists in replacing the elastic beam by a system consisting of massless rigid beams carrying lumped masses. The massless beams are connected through frictionless two-degrees of freedom joints with appropriate lateral and rotational springs in them. The method can be easy adapted to study buckling and bending vibration of flexible beams with various kinds of boundary conditions. Since the inertial characteristic of the flexible beam are represented by lumped masses, the lumped parameter method presented allows a relatively simple program implementation in some of the programming environments such as Mathematica, Matlab, Maple, etc.
UTORAK, 16.04.2019. u 17:00, Sala 301f, MI SANU, Kneza Mihaila 36
Marija Mikić, Faculty of Mathematics, Belgrade, Serbia
ASYMPTOTIC PROPERTIES OF SOLUTIONS OF EMDEN-FOWLER EQUATIONS AND THEIR GENERALIZATIONS
Emden-Fowler differential equation came first into prominence in connection with the astrophysical researcher Emden. A number of results obtained by Emden in the usual half-intuitive, wholly ingenious fashion of the physicist were made by Fowler, who was then stimulated to continue and give a complete discussion of solutions of this equation for all values of the parameters. The equation has several very interesting physical applications, occurring in astrophysics in the form of the Emden equation and in atomic physics in the form of Fermi-Thomas equation.
Mathematically, the equation has great potential. It is a nonlinear differential equation with a large class of solutions whose behavior can be ascertained with astonishing accuracy, despite the fact that the solutions, in general, can’t be obtained explicitly. The Emden-Fowler type of equation has significant applications in many fields of scientific and technical world and this equation has been investigated by many researchers.
The subject of this lecture is the investigation of asymptotic properties of solutions for differential equations of Emden-Fowler type and their generalizations. The conditions, which provide that this equation has infinitely many solutions defined in some neighborhood of zero, were described here, both with the conditions, which guarantee the existence of infinitely many solutions with certain asymptotic behavior. Also, a complete picture of the asymptotic behavior of solutions of the equation along the positive parts of both axes is given. The conditions, which assure existence and unique solvability of a solution of the Cauchy problem for this equation, were shown in the cases when the familiar theory can't be applied.
UTORAK, 23.04.2019. u 17:00, Sala 301f, MI SANU, Kneza Mihaila 36
Snežana Ćirić-Kostić, Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, Kraljevo, Serbia
ADVANCED DESIGN RULES FOR OPTIMAL DYNAMIC PROPERTIES OF ADDITIVE MANUFACTURING PRODUCTS
Additive manufacturing (AM) technologies are based on the principle of production by addition of subsequent layers of material (therefore the nickname “layer-by-layer” manufacturing for AM) without use of tools for shaping or removing of material. This production principle enables production without majority of design constraints imposed by conventional production technologies, making AM technologies suitable for the production of parts with complex geometry (lattice and cellular design, bionic design, multi functionality integrated by shape, etc.) and opening new possibilities for innovation in design. Having in mind the consequential differences in microstructure, it is necessary to study the static and dynamic behaviour of parts manufactured by AM in accordance with the relevant standards before the parts may be used under the similar exploitation conditions as the parts produced by traditional technologies. While the static characteristics of AM parts have been largely studied during the first decade of the 21st century, dynamic behaviour studies began only in this decade, still with scarce and not systematized results.
The goal of the lecture is to present the results of studies of dynamic behaviour of steel parts produced by direct metal laser sintering (DMLS) performed within the framework of the H2020 project A_MADAM. The lecture consists of presentation of the research plan of the project, followed by overview and discussion of the results of testing the influence of the technology parameters on the fatigue behaviour of maraging steel and stainless steel parts produced by DMLS. The objective of the project is to understand the dependencies between the characteristics of the production process and the observed fatigue behaviour of the tested samples, thus opening the possibilities for optimizations from two aspects: 1) optimization of the product design with respect to the production process and 2) optimization of the production process in relation to product design.
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.
Prof. dr Katica (Stevanović) Hedrih
dr Ivana Atanasovska