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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

The influence of geometric imperfections on the stability of three-layer beams with foam core

Wstawska I.

Archives of Mechanical Technology and Materials

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2017

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Vol. 37

65--69

EN

The main objective of this work is the numerical analysis (FE analysis) of stability of three-layer beams with metal foam core (alumina foam core). The beams were subjected to pure bending. The analysis of the local buckling was performed. Furthermore, the influence of geometric parameters of the beam and material properties of the core (linear and non-linear model) on critical loads values and buckling shape were also investigated. The calculations were made on a family of beams with different mechanical properties of the core (elastic and elastic-plastic material). In addition, the influence of geometric imperfections on deflection and normal stress values of the core and the faces has been evaluated.

3

Modelowanie belek pięciowarstwowych

Magnucki K., Jasion P., Smyczyński M.

Modelowanie Inżynierskie

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2012

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T. 14, nr 45

90--98

PL

W pracy przedstawiono model belki trójwarstwowej, w którym uwzględniono cienkie warstwy kleju łączące okładziny z rdzeniem. Sformułowano całkowitą energię potencjalną belki, a z zasady stacjonarności tej energii wyznaczono układ równań różniczkowych równowagi. Układ ten rozwiązano i wyznaczono ugięcie belki. Wyniki rozwiązania analitycznego porównano z wynikami numerycznymi MES. Zamieszczono przegląd literatury z uwzględnieniem współczesnych badań.

EN

The subject of the paper is an analysis of deflection of a five layer sandwich beam. The mechanical and physical properties vary through the thickness of the beam and depend on the material of each layer, which are: the metal face, binding material (the glue) and metal foam core. The main aim of the paper is to present an analytical model of the five layer beam and to compare the results of the analyses obtained theoretically and numerically. Moreover, the proposed model is compared with a three layer sandwich beam model. In the paper a mathematical model of the field of displacements, which include a share effect and a bending moment, is presented. The system of partial differential equations of equilibrium for the five layer sandwich beam is derived on the basis of the principle of stationary total potential energy. The equations are analytically solved and deflection is obtained. The influence of the binding layer thickness and Young’s modulus on the value of deflection is analysed. Comparison of the results obtained in the analytical and numerical (MES) analysis are shown in graphs and figures.

4

Wyboczenie-zmarszczenie okładziny belki trójwarstwowej przy czystym zginaniu

Jasion P., Magnucki K.

Modelowanie Inżynierskie

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2011

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T. 10, nr 41

151-156

PL

Przedmiotem pracy są belki trójwarstwowe poddane czystemu zginaniu. Opisano i rozwiązano problem wyboczenia-zmarszczenia okładziny ściskanej. Równanie równowagi wyznaczono z zasady stacjonarności całkowitej energii potencjalnej, którego całką są funkcje hiperboliczne. Badania numeryczne przeprowadzono dla rodziny belek o różnych właściwościach mechanicznych rdzenia. Ponadto przeprowadzono badania numeryczne MES. Obciążenia krytyczne otrzymane z obu metod zestawiono w tabelach i na wykresach.

EN

The subject of the paper are sandwich beams under pure bending. The problem of buckling-wrinkling of a compression face is described and solved. The equation of equilibrium is obtained based on the principle of stationary total potential energy. The analytical solution of this equation is composed of hyperbolic functions. Numerical calculations are realized for a family of sandwich beams with different mechanical properties of the core. Moreover, FEM investigations are realized. Results of both methods are compared and presented in tables and figures.

5

Mshhnihst' ta deformashhjjnihst' trisharovikh zalihzobetonnikh balkovikh konstrukcihjj ihz zovnihshnihm listovim armuvannjam

Barabash V. M., Shmig R.

Zeszyty Naukowe Politechniki Rzeszowskiej. Budownictwo i Inżynieria Środowiska

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2000

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z. 32[180], cz.1

25-32

EN

The thesis comprising the experimental theoretical investigations of new common and preliminary tensed complex concrete reinforced constructions. The basis of the suggested solution is the panel construction which is composed of the reinforced pressed up layer and the stretched lower layer reinforced with the external band skeleton frame construction, the space between which is filled with the light heat isolation keramzite-concrete. It was estimated that the great importance for the proper work with the bend three-layer steel concrete constructions is the connection between the layers of different concrete, the presence of space frame systems on the supporting and the bend anchors in their flight of cutting. The suggested mathematic model according to the method of final elements defines the tense-deformed state of the complex concrete reinforced constructions regarding the real programs of materials deformation at all loading stages.