Analysis of thin-walled beams with variable monosymmetric cross section by means of Legendre polynomials

• Autorzy: Szybiński Józef , Ruta Piotr

Identyfikatory

DOI

10.2478/sgem-2019-0001

• Języki publikacji: EN

Abstrakty

EN

This article deals with the vibrations of a nonprismatic thin-walled beam with an open cross section and any geometrical parameters. The thin-walled beam model presented in this article was described using the membrane shell theory, whilst the equations were derived based on the Vlasov theory assumptions. The model is a generalisation of the model presented by Wilde (1968) in ‘The torsion of thin-walled bars with variable cross-section’, Archives of Mechanics, 4, 20, pp. 431–443. The Hamilton principle was used to derive equations describing the vibrations of the beam. The equations were derived relative to an arbitrary rectilinear reference axis, taking into account the curving of the beam axis and the axis formed by the shear centres of the beam cross sections. In most works known to the present authors, the equations describing the nonprismatic thin-walled beam vibration problem do not take into account the effects stemming from the curving (the inclination of the walls of the thin-walledcross section towards to the beam axis) of the analysed systems. The recurrence algorithm described in Lewanowicz’s work (1976) ‘Construction of a recurrence relation of the lowest order for coefficients of the Gegenbauer series’, Applicationes Mathematicae, XV(3), pp. 345–396, was used to solve the derived equations with variable coefficients. The obtained solutions of the equations have the form of series relative to Legendre polynomials. A numerical example dealing with the free vibrations of the beam was solved to verify the model and the effectiveness of the presented solution method. The results were compared with the results yielded by finite elements method (FEM).

Słowa kluczowe

EN

thin-walled; free vibrations; non-prismatic; Legendre polynomials

• Wydawca: De Gruyter
• Czasopismo: Studia Geotechnica et Mechanica
• Rocznik: 2019
• Tom: Vol. 41, nr 1
• Strony: 1--12
• Opis fizyczny: Bibliogr. 23 poz., tab., rys.

Twórcy

autor

Szybiński Józef

• Wrocław University of Science and Technology, Faculty of Civil Engineering, Wrocław, Poland

autor

Ruta Piotr

• Wrocław University of Science and Technology, Faculty of Civil Engineering, Wrocław, Poland

Bibliografia

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).