MECHANICS OF MACHINES AND MECHANISMS - MODELS AND MATHEMATICAL METHODS
Plan rada Seminara Mehanika mašina i mehanizama - modeli i matematičke metode za JUN 2021.
UTORAK, 01.06.2021. u 17:00, Live stream
Shuvajit Mukherjee, College of Engineering, Swansea University, Swansea, Wales, UK
TIME DOMAIN SPECTRAL ELEMENT BASED ANALYSIS OF BEAM STRUCTURES
The time domain spectral element method (TSEM) is a combination of global spectral methods and the finite element method. This combination enables TSEM’s fast spectral convergence and flexibility of discretization like FEM. Unlike FEM, TSEM uses very high order polynomials with non-uniform node spacing. This specific kind of nodal distribution corresponds to the roots of certain polynomials (Legendre polynomials). The nodes are called Gauss–Lobatto–Legendre (GLL) nodes. The Lagrange interpolants formed based on the Lobatto node hold the discrete orthogonal property. This discrete orthogonality property leads to a diagonal mass matrix resulting in a reduction of computational cost. A stochastic time domain spectral element method (STSEM) was proposed for stochastic modelling and uncertainty quantification of beam structures. Apart from the stochastic FE, time domain spectral element-based wave finite element method was also explored to analyze periodic structures. A Timoshenko beam considering geometric, as well as material periodicity, was explored for stop band characteristics. The impact of geometric parameters on the stop bands of 1-D structures was then investigated in detail. It is shown that the stop bands can be obtained in the frequency range of interest, and its width can be varied by tuning those parameters. Also, the effect of material uncertainty was studied and the results show that randomness in density influences the bandwidth of the stop bands more than that of elastic parameters
PETAK, 15.06.2021. u 17:00, Live stream
Aleksandar Nikolić, Faculty of Mechanical and Civil Engineering in Kraljevo, University in Kragujevac
RIGID SEGMENT METHOD – REVIEW OF EXISTING METHODS AND PROPOSAL OF A NEW ONE
The method of rigid segments belongs to the group of discretization methods for the analysis of static and dynamic characteristics of elastic bodies, as well as their stability. This method is a century old. Namely, the German scientist Heinrich Hencky proposed a method of discretizing an elastic beam into rigid segments connected by appropriate springs as early as 1920. Since then, a significant number of new ideas have been published on how to discretize the elastic beam to improve the accuracy and efficiency of the method. The most important ideas will be briefly presented here. In addition to the analysis of existing methods, a new idea of discretization will be presented, the use of which would avoid some shortcomings of already existing methods. A general, 3D rigid segment model of non-uniform Euler-Bernoulli and Timoshenko beam will be formed. By using the absolute coordinates of rigid segments relative to the inertial coordinate frame, with the application of the Lagrange formalism, differential equations of motion in vector form were obtained. Based on these differential equations the eigenvalue problem was formed. The obtained model of the beam is general, so its efficiency does not depend on the law of change of material parameters or geometrical characteristics of the cross-section along the beam, which can be stated as the main disadvantage of many other methods in this field. The proposed rigid segment model has a wide application, but the focus is on the analysis of coupled transverse and axial vibrations of beams with eccentrically tip mass, as well as on the vibration analysis of cracked beams. The efficiency of the proposed method was tested through several numerical examples where the results were compared with the results obtained by applying other methods.
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