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Fabrizio Vestroni - One of the best experts on this subject based on the ideXlab platform.
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The role of nonlinear torsional contributions on the stability of flexural-torsional oscillations of Open-Cross Section beams
Journal of Sound and Vibration, 2015Co-Authors: Angelo Di Egidio, Alessandro Contento, Fabrizio VestroniAbstract:Abstract An Open-Cross Section thin-walled beam model, already developed by the authors, has been conveniently simplified while maintaining the capacity of accounting for the significant nonlinear warping effects. For a technical range of geometrical and mechanical characteristics of the beam, the response is characterized by the torsional curvature prevailing over the flexural ones. A Galerkin discretization is performed by using a suitable expansion of displacements based on shape functions. The attention is focused on the dynamic response of the beam to a harmonic force, applied at the free end of the cantilever beam. The excitation is directed along the symmetry axis of the beam Section. The stability of the one-component oscillations has been investigated using the analytical model, showing the importance of the internal resonances due to the nonlinear warping coupling terms. Comparison with the results provided by a computational finite element model has been performed. The good agreement among the results of the analytical and the computational models confirms the effectiveness of the simplified model of a nonlinear Open-Cross Section thin-walled beam and overall the important role of the warping and of the torsional elongation in the study of the one-component dynamic oscillations and their stability.
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Static behavior and bifurcation of a monosymmetric Open Cross-Section thin-walled beam: Numerical and experimental analysis
International Journal of Solids and Structures, 2011Co-Authors: Angelo Di Egidio, Fabrizio VestroniAbstract:Abstract The aim of the paper is the numerical and experimental validation of a previously developed nonlinear one-dimensional model of inextensional, shear undeformable, thin-walled beam with an Open Cross-Section. Nonlinear in-plane and out-of-plane warping and torsional elongation effects are included in the model. To better understand the role of these new contributions a beam with a Section with one symmetry axis, undergoing moderately large flexural curvatures and large torsional curvature is taken into account. To obtain a Section of a cantilever beam for which the torsional curvature is expected to prevail with respect to the flexural ones, a preliminary study is performed. The attention is focused on the response to static forces and on the stability of the equilibrium branches. Analytical results are compared with results of two different nonlinear finite element models and mainly with experimental results to confirm the validity of the analytical model. Interesting results are obtained for the critical values of the flexural–torsional instability loads.
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A non-linear model for the dynamics of Open Cross-Section thin-walled beams--Part I: formulation
International Journal of Non-Linear Mechanics, 2003Co-Authors: Angelo Di Egidio, Angelo Luongo, Fabrizio VestroniAbstract:A non-linear one-dimensional model of inextensional, shear undeformable, thin-walled beam with an Open Cross-Section is developed. Non-linear in-plane and out-of-plane warping and torsional elongation effects are included in the model. By using the Vlasov kinematical hypotheses, together with the assumption that the Cross-Section is undeformable in its own plane, the non-linear warping is described in terms of the flexural and torsional curvatures. Due to the internal constraints, the displacement field depends on three components only, two transversal translations of the shear center and the torsional rotation. Three non-linear differential equations of motion up to the third order are derived using the Hamilton principle. Taking into account the order of magnitude of the various terms, the equations are simplified and the importance of each contribution is discussed. The effect of symmetry properties is also outlined. Finally, a discrete form of the equations is given, which is used in Part II to study dynamic coupling phenomena in conditions of internal resonance.
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A non-linear model for the dynamics of Open Cross-Section thin-walled beams--Part II: forced motion
International Journal of Non-Linear Mechanics, 2003Co-Authors: Angelo Di Egidio, Angelo Luongo, Fabrizio VestroniAbstract:The discrete equations developed in Part I are here used to analyze the non-linear dynamics of an inextensional shear indeformable beam with given end constraints. The model takes into account the non-linear effects of warping and of torsional elongation. Non-linear 3D oscillations of a beam with a Cross-Section having one symmetry axis is examined. Only terms of higher magnitude are retained in the equations, which exhibit quadratic, cubic and combination resonances. A harmonic load acting in the direction of the symmetry axis and in resonance with the corresponding natural frequency, is considered. Steady-state solutions and their stability are studied; in particular the effects of non-linear warping and of torsional elongation on the response are highlighted.
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A non-linear model for the dynamics of Open Cross-Section thin-walled beams—Part I: formulation
International Journal of Non-linear Mechanics, 2002Co-Authors: Angelo Di Egidio, Angelo Luongo, Fabrizio VestroniAbstract:A non-linear one-dimensional model of inextensional, shear undeformable, thin-walled beam with an Open Cross-Section is developed. Non-linear in-plane and out-of-plane warping and torsional elongation effects are included in the model. By using the Vlasov kinematical hypotheses, together with the assumption that the Cross-Section is undeformable in its own plane, the non-linear warping is described in terms of the flexural and torsional curvatures. Due to the internal constraints, the displacement field depends on three components only, two transversal translations of the shear center and the torsional rotation. Three non-linear differential equations of motion up to the third order are derived using the Hamilton principle. Taking into account the order of magnitude of the various terms, the equations are simplified and the importance of each contribution is discussed. The effect of symmetry properties is also outlined. Finally, a discrete form of the equations is given, which is used in Part II to study dynamic coupling phenomena in conditions of internal resonance.
Angelo Di Egidio - One of the best experts on this subject based on the ideXlab platform.
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The role of nonlinear torsional contributions on the stability of flexural-torsional oscillations of Open-Cross Section beams
Journal of Sound and Vibration, 2015Co-Authors: Angelo Di Egidio, Alessandro Contento, Fabrizio VestroniAbstract:Abstract An Open-Cross Section thin-walled beam model, already developed by the authors, has been conveniently simplified while maintaining the capacity of accounting for the significant nonlinear warping effects. For a technical range of geometrical and mechanical characteristics of the beam, the response is characterized by the torsional curvature prevailing over the flexural ones. A Galerkin discretization is performed by using a suitable expansion of displacements based on shape functions. The attention is focused on the dynamic response of the beam to a harmonic force, applied at the free end of the cantilever beam. The excitation is directed along the symmetry axis of the beam Section. The stability of the one-component oscillations has been investigated using the analytical model, showing the importance of the internal resonances due to the nonlinear warping coupling terms. Comparison with the results provided by a computational finite element model has been performed. The good agreement among the results of the analytical and the computational models confirms the effectiveness of the simplified model of a nonlinear Open-Cross Section thin-walled beam and overall the important role of the warping and of the torsional elongation in the study of the one-component dynamic oscillations and their stability.
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Static behavior and bifurcation of a monosymmetric Open Cross-Section thin-walled beam: Numerical and experimental analysis
International Journal of Solids and Structures, 2011Co-Authors: Angelo Di Egidio, Fabrizio VestroniAbstract:Abstract The aim of the paper is the numerical and experimental validation of a previously developed nonlinear one-dimensional model of inextensional, shear undeformable, thin-walled beam with an Open Cross-Section. Nonlinear in-plane and out-of-plane warping and torsional elongation effects are included in the model. To better understand the role of these new contributions a beam with a Section with one symmetry axis, undergoing moderately large flexural curvatures and large torsional curvature is taken into account. To obtain a Section of a cantilever beam for which the torsional curvature is expected to prevail with respect to the flexural ones, a preliminary study is performed. The attention is focused on the response to static forces and on the stability of the equilibrium branches. Analytical results are compared with results of two different nonlinear finite element models and mainly with experimental results to confirm the validity of the analytical model. Interesting results are obtained for the critical values of the flexural–torsional instability loads.
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A non-linear model for the dynamics of Open Cross-Section thin-walled beams--Part I: formulation
International Journal of Non-Linear Mechanics, 2003Co-Authors: Angelo Di Egidio, Angelo Luongo, Fabrizio VestroniAbstract:A non-linear one-dimensional model of inextensional, shear undeformable, thin-walled beam with an Open Cross-Section is developed. Non-linear in-plane and out-of-plane warping and torsional elongation effects are included in the model. By using the Vlasov kinematical hypotheses, together with the assumption that the Cross-Section is undeformable in its own plane, the non-linear warping is described in terms of the flexural and torsional curvatures. Due to the internal constraints, the displacement field depends on three components only, two transversal translations of the shear center and the torsional rotation. Three non-linear differential equations of motion up to the third order are derived using the Hamilton principle. Taking into account the order of magnitude of the various terms, the equations are simplified and the importance of each contribution is discussed. The effect of symmetry properties is also outlined. Finally, a discrete form of the equations is given, which is used in Part II to study dynamic coupling phenomena in conditions of internal resonance.
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A non-linear model for the dynamics of Open Cross-Section thin-walled beams--Part II: forced motion
International Journal of Non-Linear Mechanics, 2003Co-Authors: Angelo Di Egidio, Angelo Luongo, Fabrizio VestroniAbstract:The discrete equations developed in Part I are here used to analyze the non-linear dynamics of an inextensional shear indeformable beam with given end constraints. The model takes into account the non-linear effects of warping and of torsional elongation. Non-linear 3D oscillations of a beam with a Cross-Section having one symmetry axis is examined. Only terms of higher magnitude are retained in the equations, which exhibit quadratic, cubic and combination resonances. A harmonic load acting in the direction of the symmetry axis and in resonance with the corresponding natural frequency, is considered. Steady-state solutions and their stability are studied; in particular the effects of non-linear warping and of torsional elongation on the response are highlighted.
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A non-linear model for the dynamics of Open Cross-Section thin-walled beams—Part I: formulation
International Journal of Non-linear Mechanics, 2002Co-Authors: Angelo Di Egidio, Angelo Luongo, Fabrizio VestroniAbstract:A non-linear one-dimensional model of inextensional, shear undeformable, thin-walled beam with an Open Cross-Section is developed. Non-linear in-plane and out-of-plane warping and torsional elongation effects are included in the model. By using the Vlasov kinematical hypotheses, together with the assumption that the Cross-Section is undeformable in its own plane, the non-linear warping is described in terms of the flexural and torsional curvatures. Due to the internal constraints, the displacement field depends on three components only, two transversal translations of the shear center and the torsional rotation. Three non-linear differential equations of motion up to the third order are derived using the Hamilton principle. Taking into account the order of magnitude of the various terms, the equations are simplified and the importance of each contribution is discussed. The effect of symmetry properties is also outlined. Finally, a discrete form of the equations is given, which is used in Part II to study dynamic coupling phenomena in conditions of internal resonance.
Luciano Feo - One of the best experts on this subject based on the ideXlab platform.
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non linear pre buckling behavior of shear deformable thin walled composite beams with Open Cross Section
Composites Part B-engineering, 2013Co-Authors: Geminiano Mancusi, Luciano FeoAbstract:Abstract A kinematic model is presented for thin-walled composite beams able to account for axial force, bending, torsion and warping. Shear deformations on the mid-surface are considered and modeled by means of a polynomial approximation. For this scope appropriate shape functions on the curvilinear abscissa along the Cross-Section mid-line are introduced. Small strains and moderate rotations are considered over the pre-buckling range. The model allows to predict the static non-linear behavior and the critical loads of composite pultruded beams. A finite element approximation is derived from a variational approach. Some numerical results are also presented revealing the importance of the shear terms on the mechanical response and their effect on the stability of pultruded composite members.
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Modeling shear deformability of thin-walled composite beams with Open Cross-Section
Mechanics Research Communications, 2010Co-Authors: Luciano Feo, Geminiano MancusiAbstract:Abstract The present work formulates a one-dimensional kinematical model capable of assessing the statical behaviour of fibre-reinforced polymers (FRP) thin-walled beams with Open Cross-Section. The proposed model accounts for the effects of shear deformability. Numerical results computed via finite element method (FEM) are provided and compared with the classical ones predicted by Vlasov’s theory. It is concluded that shear deformability can provoke deflections exceeding the values predicted by the classical thin-walled beam theory. Therefore, the proposed model seems to represent a viable alternative to assess the behaviour of such structures.
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ON THE MECHANICAL BEHAVIOUR OF THIN-WALLED BEAMS OF Open Cross-Section: AN ELASTIC NON-LINEAR THEORY
International Journal of Computational Engineering Science, 2001Co-Authors: Luigi Ascione, Luciano FeoAbstract:A general one-dimensional model able to study thin-walled beams of Open Cross-Section, exhibiting moderate angles of twist, is presented. It is derived from the 3-D continuous model assuming that the beam Cross-Section presents a rigid deformation in, and warps out, its own plane. Comparisons with a previous model proposed by Ghobarah and Tso are also made.
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ON THE NON-LINEAR STATICAL BEHAVIOUR OF THIN-WALLED ELASTIC BEAMS OF Open Cross-Section: A NUMERICAL APPROACH
International Journal of Computational Engineering Science, 2001Co-Authors: Luigi Ascione, Luciano FeoAbstract:In this paper a numerical investigation relative to the static behaviour of thin-walled beams of Open Cross-Section, undergoing moderate angles of twist, is presented. The constitutive equations between nominal stresses and Green strains are assumed to be linear elastic and isotropic. The numerical results are obtained by using a finite element approach, following a classical Newton-Raphson procedure. They show the peculiarity of the non-linear dependence of the torsional torque on the corresponding angle of rotation, which can be either of hardening or softening type. Comparisons with previous numerical results available in literature are also provided.
Aleksandar Prokić - One of the best experts on this subject based on the ideXlab platform.
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An improved analysis of free torsional vibration of axially loaded thin-walled beams with point-symmetric Open Cross-Section
Applied Mathematical Modelling, 2016Co-Authors: Aleksandar Prokić, Rastislav Mandić, Martina Vojnić-purčarAbstract:Abstract The objective of the paper is to analyze the influence of bimoment induced by constant axial loads on the free motion of thin-walled beams with point-symmetric Open Cross-Section. For various boundary conditions, a closed-form solution for natural frequencies of free harmonic vibrations was derived by using a general solution of governing differential equations of motion based on Vlasov's theory. In order to investigate the effect of the bimoment on natural frequencies, the numerical examples with symmetric Z Cross-Section are given. The obtained results, verified using an ANSYS finite element model, demonstrate that the influence of the bimoment is important in the assessment of torsional natural frequencies.
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Free Vibration Analysis of Cross-Ply Laminated Thin-Walled Beams with Open Cross Sections: Exact Solution
Journal of Structural Engineering, 2013Co-Authors: Aleksandar Prokić, Dragan Lukić, Ilija M. MiličićAbstract:AbstractThe objective of the present paper is to analyze the free vibrations of thin-walled beams with arbitrary Open Cross Section, made of Cross-ply laminates with midplane symmetry, by means of an exact solution. The theory of thin-walled composite beams is based on assumptions consistent with Vlasov’s beam theory and classical lamination theory. The governing differential equations for coupled bending-torsional vibrations were obtained using the principle of virtual displacements. To simplify the coupled system of differential equations, an ideal center of gravity and shear center were introduced. In the case of a simply supported thin-walled beam, the closed-form solution for the natural frequencies of free harmonic vibrations was derived. The frequency equation, given in determinantal form, is expanded in an explicit analytical form. To demonstrate the validity of this method, the natural frequencies of nonsymmetric thin-walled beams having coupled deformation modes are evaluated and compared with r...
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Effect of Bracing on Linear Free Vibration Characteristics of Thin-Walled Beams with Open Cross Section
Journal of Engineering Mechanics, 2010Co-Authors: Aleksandar ProkićAbstract:The paper presents an analysis of the coupled vibration of beams with arbitrary thin-walled Open Cross Section, braced with identical transversal header beams uniformly distributed along their length. The explicit form of analytic solution is derived by directly solving the governing differential equations of motion. The development is based on Vlasov theory which includes the effect of flexural-torsion coupling, the constrained torsion warping, and rotary inertia. The governing differential equations for coupled bending-torsional vibrations are performed using the principle of virtual displacements. In the case of simply supported beam, exact explicit expressions are derived to predict the natural frequencies and the corresponding mode shapes. The frequency equation, given in determinantal form, is expanded in an explicit analytical form, and then solved using the symbolic computing package Mathcad. The expressions are concise and very simple and as such convenient to be used by a practicing engineer who does not need to go into detail of thin-walled beam theory. Also, the use of explicit expressions gives significant savings in computing time compared with the alternative numerical methods [finite-element method (FEM), finite strip method, differential transform method, etc.]. To demonstrate the validity of this method the natural frequencies of braced thin-walled beams, having coupled deformation modes, are evaluated and compared with FEM.
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On triply coupled vibrations of thin-walled beams with arbitrary Cross-Section
Journal of Sound and Vibration, 2005Co-Authors: Aleksandar ProkićAbstract:The purpose of this paper is to analyze triply coupled vibrations of thin-walled beams with arbitrary Open Cross-Section. Starting from the Vlasov's theory, the governing differential equations for coupled bending and torsional vibrations were performed using the principle of virtual displacements. In the case of a simply supported thin-walled beam, a closed-form solution for the natural frequencies of free harmonic vibrations was derived. The significance of neglecting Cross-Sectional warping and rotary inertia on the accuracy of results was analyzed. A recent paper on the same subject is discussed, with a critical review of it.
Geminiano Mancusi - One of the best experts on this subject based on the ideXlab platform.
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non linear pre buckling behavior of shear deformable thin walled composite beams with Open Cross Section
Composites Part B-engineering, 2013Co-Authors: Geminiano Mancusi, Luciano FeoAbstract:Abstract A kinematic model is presented for thin-walled composite beams able to account for axial force, bending, torsion and warping. Shear deformations on the mid-surface are considered and modeled by means of a polynomial approximation. For this scope appropriate shape functions on the curvilinear abscissa along the Cross-Section mid-line are introduced. Small strains and moderate rotations are considered over the pre-buckling range. The model allows to predict the static non-linear behavior and the critical loads of composite pultruded beams. A finite element approximation is derived from a variational approach. Some numerical results are also presented revealing the importance of the shear terms on the mechanical response and their effect on the stability of pultruded composite members.
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Modeling shear deformability of thin-walled composite beams with Open Cross-Section
Mechanics Research Communications, 2010Co-Authors: Luciano Feo, Geminiano MancusiAbstract:Abstract The present work formulates a one-dimensional kinematical model capable of assessing the statical behaviour of fibre-reinforced polymers (FRP) thin-walled beams with Open Cross-Section. The proposed model accounts for the effects of shear deformability. Numerical results computed via finite element method (FEM) are provided and compared with the classical ones predicted by Vlasov’s theory. It is concluded that shear deformability can provoke deflections exceeding the values predicted by the classical thin-walled beam theory. Therefore, the proposed model seems to represent a viable alternative to assess the behaviour of such structures.
