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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

Diffusion equation including a local fractional derivative and weighted inner product

Cetinkaya Suleyman, Demir Ali

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 1

19--27

EN

In this research, we discuss the construction of the analytic solution of the homogenous initial boundary value problem including partial differential equations of fractional order. Since the homogenous initial boundary value problem involves a local fractional order derivative, it has classical initial and boundary conditions. By means of separation of the variables method and the inner product defined on L2 [0, l], the solution is constructed in the form of a Fourier series including the exponential function. The illustrative examples present the applicability and influence of the separation of variables method on time fractional diffusion problems. Moreover, as the fractional order α tends to 1, the solution of the fractional diffusion problem tends to the solution of the diffusion problem which proves the accuracy of the solution.

3

Large-signal averaged models of the non-ideal flyback converter derived by the separation of variables

Janke W., Bączek M., Kraśniewski J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2020

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Vol. 68, nr 1

81--88

EN

The main topic of the paper is the large signal averaged model of a switch-mode flyback power converter. The use of the large-signal averaged models of switching converters allows for fast simulation of power systems. The known averaged models of a flyback are based on the state-space averaging or switch-averaging approach. The model presented in the paper is derived with the use of the separation of variables approach and include parasitic resistances of all converter components. The limitations of the model accuracy are discussed. The calculations based on the averaged model are compared with detailed full-wave simulations and measurements results.

4

Small-signal transmittances of DC-DC step-down PWM converter in various operation modes

Janke W.

Archives of Electrical Engineering

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2015

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Vol. 64, nr 3

505--529

EN

Small-signal transmittances: input-to-output and control-to-output of BUCK converter power stage working in CCM or DCM mode are discussed. Ideal converter case and converter with parasitic resistances are considered separately. Derivations of small-signal transmittances, based on different approaches to finding the converter averaged models, are presented and the results are compared. Apart from theoretical considerations, some results of numerical calculations are presented.