Nonlinear analysis of thin-walled members of variable cross-section. Part I: Theory

2000 ◽  
Vol 77 (3) ◽  
pp. 285-299 ◽  
Author(s):  
H.R. Ronagh ◽  
M.A. Bradford ◽  
M.M. Attard
Keyword(s):  
Nonlinear Analysis ◽  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Thin Walled ◽  
Cross Section Part

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

2019 ◽  
Vol 41 (1) ◽  
pp. 1-12
Author(s):  
Józef Szybiński ◽  
Piotr Ruta
Keyword(s):  
Cross Section ◽  
Legendre Polynomials ◽  
Variable Cross Section ◽  
Free Vibrations ◽  
Variable Coefficients ◽  
Beam Axis ◽  
Geometrical Parameters ◽  
Beam Model ◽  
Variable Cross ◽  
Thin Walled

AbstractThis 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).

scholarly journals Vibration and Stability of Variable Cross Section Thin-Walled Composite Shafts with Transverse Shear

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Ma Jing-min ◽  
Ren Yong-sheng
Keyword(s):  
Shear Deformation ◽  
Cross Section ◽  
Transverse Shear ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Rotating Speed ◽  
Composite Shaft ◽  
Variational Asymptotic ◽  
Finite Element Package ◽  
Thin Walled

A dynamic model of composite shaft with variable cross section is presented. Free vibration equations of the variable cross section thin-walled composite shaft considering the effect of shear deformation are established based on a refined variational asymptotic method and Hamilton’s principle. The numerical results calculated by Galerkin method are analyzed to indicate the effects of ply angle, taper ratio, and transverse shear deformation on the first natural frequency and critical rotating speed. The results are compared with those obtained by using finite element package ANSYS and available in the literature using other models.

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