Wyniki wyszukiwania - BazTech

1

Exact solutions of fractional oscillator eigenfunction problem with fixed memory length

Klimek Malgorzata, Blaszczyk Tomasz

Journal of Applied Mathematics and Computational Mechanics

|

2024

|

Vol. 23, nr 1

45-58

EN

In this paper, the eigenproblem for a fractional oscillator under homogeneous Dirichlet and Neumann boundary conditions is considered. Key properties of fractional operators with fixed memory length are established, such as the connection between left and right operators, the product rule for fractional integrals, and the fractional integration by the parts rule for periodic/antiperiodic functions. Explicit solutions in the form of discrete sets of sine/cosine eigenfunctions are derived. The impact of fractional order and memory length on eigenvalues is presented on graphs. Finally, a comparison of eigenvalues of oscillator with a fixed memory length and infinite memory length is shown.

2

Stability of the thin-walled angle column made of bio-laminate versus glass-laminate under axial compression – numerical study

Gawryluk Jarosław

Archive of Mechanical Engineering

|

2023

|

LXX, nr 1

43--61

EN

The aim of this study was to determine how the change of glass laminate fibres to flax fibres will affect the stability of thin-walled angle columns. Numerical analyses were conducted by the finite element method. Short L-shaped columns with different configurations of reinforcing fibres and geometric parameters were tested. The axially compressed structures were simply supported on both ends. The lowest two bifurcation loads and their corresponding eigenmodes were determined. Several configurations of unidirectional fibre arrangement were tested. Moreover, the influence of a flange width change by ±100% and a column length change by ±33% on the bifurcation load of the compressed structure was determined. It was found that glass laminate could be successfully replaced with a bio-laminate with flax fibres. Similar results were obtained for both materials. For the same configuration of fibre arrangement, the flax laminate showed a lower sensitivity to the change in flange width than the glass material. However, the flax laminate column showed a greater sensitivity to changes in length than the glass laminate one. In a follow-up study, selected configurations will be tested experimentally.

3

Numerical simulation of random fields using correlated random vector and the Karhunen-Loève expansion

Poński M., Pokorska I.

Computer Assisted Methods in Engineering and Science

|

2018

|

Vol. 25, no. 1

47--58

EN

The paper presents an approach of one- and two-dimensional random fields simulation methods using correlated random vector and Karhunen-Loève expansion. Comparison of the authors’ analytical solution of the Fredholm integral equation of the second kind with the numerical solution using finite element method and inverse vector iteration technique is presented. Numerical approach and sample realizations of one- and two-dimensional random fields are presented using described techniques as well as generated probability distribution functions for chosen point of analyzed domain.

4

Rozwiązanie zagadnienia własnego dla niepryzmatycznego łuku kołowego z wykorzystaniem szeregów Czebyszewa

Ruta P., Meissner M.

Czasopismo Inżynierii Lądowej, Środowiska i Architektury / Journal of Civil Engineering, Environment and Architecture

|

2013

|

z. 60, nr 1

161--173

PL

Przedmiotem analizy jest zagadnienie własne luku kołowego o zmiennym przekroju, opisane według teorii Bernoulliego-Eulera. Problem jest rozwiązywany z wykorzystaniem metody aproksymacyjnej, w której do aproksymacji wykorzystuje się szeregi wielomianów Czebyszewa I rodzaju. Zastosowana w pracy metoda jest oparta na ogólnym twierdzeniu opisującym związki rekurencyjne dla równań różniczkowych o zmiennych współczynnikach. Metoda ta prowadzi do wyznaczenia nieskończonego układu równań algebraicznych, którego współczynniki są określone zamkniętymi formułami analitycznymi. Formuły te w sposób jawny zależą od wyrazów szeregów, w które rozwinięto zmienne współczynniki wyjściowych równań różniczkowych. Otrzymana w ten sposób ogólna postać równań algebraicznych pozwala na rozwiązanie analizowanego zagadnienia dla dowolnych geometrycznych parametrów łuku, takich jak: krzywizna, zmienne pole i zmienny moment bezwładności przekroju czy gęstość łuku. Do analitycznych formuł opisujących współczynniki układu równań algebraicznych wystarczy bowiem podstawić współczynniki szeregów opisujących parametry materiałowe i geometryczne łuku. W celu weryfikacji poprawności oraz skuteczności otrzymanego algorytmu uzyskane prezentowaną w pracy metodą częstości i formy własne porównano z wynikami uzyskanymi metodą elementów skończonych. Obliczenia wykonano programem Cosmos/M, stosując do aproksymacji elementy belkowe 3D o liniowo zmiennym przekroju. W celu oceny różnicy między formami własnymi wyznaczono dla nich standardowy indeks MAC (Modal Assurance Criterion). Otrzymane rezultaty potwierdziły poprawność oraz skuteczność omawianej w pracy metody.

EN

The subject of analysis is eigenproblem of circular arch with variable cross-sections, described by the Bernoulli-Euler theory. The problem is solved using approximation method, in which Chebyshev polynomials of first kind series are used. Method used in paper is based on general theorem describing recursive relationships for differential equations with variable coefficients. This method leads to the designation of an infinite system of algebraic equations, coefficients of which are defined by closed analytical formulas. These formulas depend explicitly on terms of the series, which are expansions of the variable coefficients of output differential equations. Thus obtained the general form of algebraic equations allows one to solve analysed problem for any geometrical arch parameters such as: curvature, variable cross-section area and moment of inertia, or arch density. It is enough to substitute coefficients of the series describing material and geometrical parameters to analytical formulas describing coefficients of the system of algebraic equations. In order to verify the effectiveness and correctness of obtained algorithm natural frequencies and eigenforms received from presented method were compared to the results obtained with the finite element method. Calculations were made in Cosmos/M program using 3D beam elements with linearly variable cross-section for approximation. In order to evaluate differences between eigenforms the standard MAC (Modal Assurance Criterion) index was designated. The obtained results confirmed effectiveness and correctness of the method presented in paper.

5

The dynamics of an ideal fluid flow into an inclined cavity of a paraboloid form

Filip D., Trimbitas R., Pop I.

International Journal of Applied Mechanics and Engineering

|

2001

|

Vol. 6, no 4

947-968

EN

The present paper is a theoretical study of the motion of an inclined cavity of a paraboloid form filled with an ideal and incompressible fluid. The cavity is placed in the gravity field and its roto-translation motion is unknown. We look for determining the translation and rotation velocities of the cavity, the velocity potential of the fluid particles as well as the form of the fluid free surface. To this end, we shall use both the analytical and numerical methods. Numerical examples are presented in tables and graphs to elucidate the accuracy and efficiency of the proposed method.