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1
Content available Dynamic stability of a three-layer beam – generalisation of the sandwich structure theory
Magnucki Krzysztof, Magnucka-Blandzi Ewa
Acta Mechanica et Automatica
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2024
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Vol. 18, no. 1
1--7
EN
The work focuses on the dynamic stability problem of a simply supported three-layer beam subjected to a pulsating axial force. Two analytical models of this beam are developed: one model takes into account the non-linear hypothesis of cross-section deformation, and the other takes into account the standard "broken line" hypothesis. Displacements, strains and stresses for each model are formulated in detail. Based on the Hamilton principle, equations of motion are determined for each of these models. These systems of two differential equations for each model are approximately solved with the consideration of the axial pulsating force, and the fundamental natural frequencies, critical forces and the Mathieu equation are determined. Detailed studies are performed for an exemplary family of beams. The stable and unstable regions are calculated for the three pulsating load cases. The values of fundamental natural frequencies and critical forces of exemplary beams calculated from two models are compared.
2
Content available Three-point bending of a beam with non-homogeneous structure in the depth direction
Magnucki Krzysztof, Magnucka-Blandzi Ewa, Witkowski Dawid, Wittenbeck Leszek
Engineering Transactions
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2023
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Vol. 71, iss. 4
645--665
EN
This paper is devoted to the behavior of a non-homogeneous simply supported beam under three-point bending. The individual shear deformation function of a planar cross-section is adopted, and longitudinal displacements, strains, and stresses for two parts of the beam are explained. By applying the principle of stationary potential energy, a system of two differential equations of equilibrium is derived and solved analytically. The positions of the neutral axis, shear coefficients, and deflections are then calculated for three different beam families. Additionally, the bending problem of these beams is studied numerically using the finite element method (FEM). The results of both analytical and numerical calculations are presented in tables and figures. The main contribution of this paper lies in the development of an analytical model incorporating the individual shear deformation function and a numerical FEM model for this beam.
3
Content available Three models of a sandwich beam: bending, buckling, and free vibrations
Magnucki Krzysztof, Magnucka-Blandzi Ewa, Wittenbeck Leszek
Engineering Transactions
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2022
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Vol. 70, iss. 2
97--122
EN
This paper is devoted to the analytical modelling of a sandwich beam. Three models of this beam are elaborated. Two nonlinear individual shear theories of deformation of a plane cross-sections are proposed. Based on Hamilton’s principle, two differential equations of motion for each model are obtained. The bending, buckling and free flexural vibration problems of the simply-supported sandwich beam considering these three models are studied. The results of these analytical investigations are presented in tables.
4
Content available Three-point bending of an expanded-tapered beam with consideration of the shear effect
Magnucki Krzysztof, Lewiński Jerzy, Magnucka-Blandzi Ewa, Stawecka Hanna
Journal of Theoretical and Applied Mechanics
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2020
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Vol. 58 nr 3
661--672
EN
The paper is devoted to an expanded-tapered beam of rectangular cross section subjected to three-point bending. The analytical model of the beam is formulated with consideration of a non-linear hypothesis of the cross section deformation. The problem of shear stress distribution in the beam is analysed based on the above mentioned hypothesis. Moreover, a numerical FEM model (SolidWorks) is developed. Examplary computations have been carried out based on the analytical and numerical models.
5
Content available remote Bending of beams with consideration of a seventh-order shear deformation theory
Magnucki Krzysztof, Stawecki Włodzimierz, Magnucka-Blandzi Ewa
Engineering Transactions
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2020
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Vol. 68, iss. 2
119--135
EN
The subject of the paper is a simply-supported prismatic beam with bisymmetrical crosssections under non-uniformly distributed load. The shapes of the cross-sections and the nonuniformly distributed load are described analytically. The individual seventh-order shear deformation theory-hypothesis of the planar beam cross-sections is assumed. Based on the principle of stationary potential energy two differential equations of equilibrium are obtained. The system of the equations is analytically solved, and the shear and deflection coefficients of the beam are derived. Moreover, the shear stress patterns for selected cross-sections are determined and compared with stresses determined by Zhuravsky’s formula. The results of example calculations are presented in tables and figures.
6
Content available remote A shear deformation theory of beams with bisymmetrical Cross-sections based on the Zhuravsky shear stress formula
Magnucki Krzysztof, Lewinski Jerzy, Magnucka-Blandzi Ewa
Engineering Transactions
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2020
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Vol. 68, iss. 4
353--370
EN
This paper is devoted to simply supported beams with bisymmetrical cross-sections under a generalized load. Based on the Zhuravsky shear stress formula, the shear deformation theory of a planar beam cross-section is formulated. The deflections and the shear stresses of exemplary beams are determined. Moreover, the numerical-FEM computations of these beams are carried out. The results of the research are shown in figures and tables.
7
Content available remote Analytical and numerical studies of an unsymmetrical sandwich beam – bending, buckling and free vibration
Magnucki Krzysztof, Magnucka-Blandzi Ewa, Lewiński Jerzy, Milecki Szymon
Engineering Transactions
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2019
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Vol. 67, iss. 4
491--512
EN
The subject of the paper is an unsymmetrical sandwich beam. The thicknesses and mechanical properties of the beam faces are different. Mathematical model of the beam is formulated based on the classical broken-line hypothesis. The equations of motions of the beam is derived on the ground of the Hamilton’s principle. Bending, buckling and free-vibration are studied in detail for exemplary unsymmetrical structure of the beam. The values of deflection, critical force and natural frequency are determined for the selected beam cases. Moreover, the same examples are computed with the use of two FEM systems, i.e. SolidWorks and ABAQUS, in order to compare the analytical and numerical calculation. The results are presented in tables and figures.
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