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Fredholm - Volterra integral equation in three dimensional problem with Macdonald kernel

100%

El-Bary A.

tom z. 26 [199]

59-65

Regular and singular asymptatic method are applied to three dimensional Fredholm-Volterra integral equation of the first kind. In this paper we constract Fredholm-Volterra integri equation in three dimensional contact problem with Macdonald kernel in many cases of contact problem.

Hybrid asymtotic method for the effect of local thickness defects and initial imperfections on the buckling of cylindrical shells

100%

Gristchak V. Z. , Golovan O. A.

Journal of Theoretical and Applied Mechanics

2003

tom Vol. 41 nr 3

509-520

A double asymptotic method for the effect of local thickness defects and initial imperfections on the buckling problems of some mechanical systems is proposed. asymptotic formulas for the critical buckling load parameter are obtained with the perturbation technique.

W pracy zaprezentowano podwójnie asymptotyczną metodę szacowania wpływu początkowych zaburzeń strukturalnych i lokalnych uszkodzeń zmieniających grubość na wyboczenie wybranych układów mechanicznych. Zastosowane wyrażenia asymptotyczne pozwalające na określenie krytycznych parametrów wyboczenia otrzymano techniką perturbacyjną.

Two approaches in the analytical investigation of the spring pendulum

86%

Sypniewska-Kamińska G. , Starosta R. , Awrejcewicz J.

tom Vol. 29

art. no. 2018005

Dynamics of the nonlinear spring pendulum is analysed using two asymptotic approaches. The multiple scale method is commonly applied with using two time scales. The purpose of the research is to justify the introduction of an additional third scale. Results of the analysis clearly show that introducing the third scale improve correctness of the approximate analytical solution. The obtained results allow for qualitative and quantitative analysis of the behavior of the studied system with a high accuracy. Calculations are made both in the neighbourhood of the resonance and also far from it.

Nonlinear vibrations of orthogonal mechanism of shaking table

72%

Bissembayev K. , Iskakov Z.

International Journal of Applied Mechanics and Engineering

2014

tom Vol. 19, no. 3

487--501

The dynamics of orthogonal mechanism in the presence of a shaking table of fixed cargo is studied. The focus is on the vibrational motion of the mechanism in slow-speed motor rotation. The analysis of the solutions for motion nonlinear equations showed that the angular velocity of the guiding link oscillates according to the harmonic law about a mean value. The character of changing its amplitude, depending on the weight of the cargo and the length of the guiding link, is determined. Dependence of the mean angular velocity on the motor torque is set.