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Consideration of shear, rotational inertia and compressive force during transverse vibrations of structural beam elements

Orobey Viktor, Nemchuk Oleksii, Lymarenko Oleksandr, Piterska Varvara, Sherstiuk Olha, Semenov Pavlo

Diagnostyka

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2024

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Vol. 25, No. 1

art. no. 2024101

EN

The procedure for taking into account shear and rotational inertia in the case of transverse vibrations of beam elements of material handling vehicles with different conditions of fastening (support) is considered. The dynamic model of the rod element is supplemented with compressive forces with a fixed line of action and monitors the angle of rotation of the rod. The Fourier method of separation of variables in the harmonic vibrations of beams is applied. This made it possible to obtain a differential equation, kinematic and static parameters in the amplitude state. The resulting differential equation is integrated, the fundamental functions are normalized, and the complete solution is presented in matrix form with initial parameters. Four cases of fundamental functions are revealed. For beam elements with different support conditions, the vibration frequency has been refined. With hinged support, the first 5 frequencies of this work coincide with the frequencies obtained by another approach.

2

Metody falkowe analizy sygnałów

Niedziela T.

Logistyka

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2014

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nr 6

7788--7796

PL

Zaproponowano metody falkowe analizy sygnałów 1-D, 2-D oraz 3-D. Przedstawienie „lądu” transformaty falkowej w postaci „lasu” transformat falkowych składającego się z” lasu” aproksymacji i trzech „lasów” detali (poziomego, pionowego i diagonalnego) pozwala na szybką detekcję punktów osobliwych z obrazów o wysokim poziomie szumów. „Drzewo aproksymacyjne” stanowi zbiór aproksymacji wieloskalowej, a „drzewo szczegółów” jest zbiorem detali współczynników odpowiednich orientacji. Skuteczność metody falkowej zilustrowano na przykładzie kompresji obrazów kolorowych.

EN

In the paper the wavelet methods of 1-D 2-D 3-D signal analyzing are presented. Wavelet transforms are presented in the "transform forest" form consisting of approximation "forest" given by the "sub forest" details : horizontal, vertical and diagonal. In the pictures which is embedded in large noises this allows the quick detection of singular points. Proposed approximation tree makes a set of multi-scaling approximations in which the tree details make a set of coefficient details for selected orientations. Effectiveness of proposed wavelet method was illustrated on the compression example of the color pictures.

3

The Fourier method in three-dimensional dynamical problems of the hemitropic theory of elasticity

Bezhuashvili Y., Rukhadze R.

Journal of Mathematics and Applications

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2012

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Vol. 35

5--21

EN

The basic three-dimensional dynamical problems for a hemitropic (non-centrally symmetric) micropolar elastic medium are considered. Using the Fourier method, the solvability of the formulated by us problems is proved in a classical sense.

4

Applicability expansion of Fourier’s method of variables separation for problem described by second order hyperbolic equation

Kasprzyk S., Urban G.

Vibrations in Physical Systems

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2002

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Vol. 20

176--177

5

Linear combinations of right invertible operators in commutative algebras with logarithms

Przeworska-Rolewicz D.

Demonstratio Mathematica

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1998

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Vol. 31, nr 4

887-898

EN

It is well known that a power of a right invertible operators is again right invertible, as well as a polynomial in a right invertible operator under appropriate assumptions. However , a linear combination of right invertible operators (in particular , their sum and/or difference) in general is not right invertible. It will be shown how to solve equations with linear combinations of right invertible operators in commutative algebras using properties of logarithmic and antilogarithmic mappings. The used method is, in a sense, a kind of the variables separation method. We shall obtain also an analogue of the classical Fourier method for partial differential equations. Note that results concerning the Fourier method are proved under weaker assumptions than those obtained in PR[l] (cf. also PR[2]). The extensive bibliography of the subject can be found in PR[2] and PR[4].