Nonlinear free vibrations of thin-walled beams in torsion

Sina, S. A.; Haddadpour, H.; Navazi, H.M.

doi:10.1007/s00707-012-0688-y

Cited by 17 publications

(4 citation statements)

References 23 publications

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“…In [11], the effect of rotary and warping inertia is considered. Nonlinear torsional vibrations of thin-walled beams, exhibiting primary and secondary warping, are investigated in [12]. A solution for the vibrations of Timoshenko beams by the isogeometric approach is presented in [13].…”

Section: Introductionmentioning

confidence: 99%

Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

Aminbaghai

Muŕın

Balduzzi

et al. 2017

Engineering Structures

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In this paper, the influence of the variable axial force and of the Secondary Torsion-Moment Deformation-Effect (STMDE) on the deformations of beams due to torsional warping is investigated. The investigation is based on the second-order torsional warping theory of doubly symmetric beams with thin-walled open or closed cross-sections. The effect of the axial force on the torsional stiffness of thinwalled beams is considered according to the second-order torsional warping theory. The solutions of the underlying differential equations are used for setting up the relations, needed for application of the transfer matrix method. They are derived, considering both static and dynamic action. This enables stablishing the local

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Section: Introductionmentioning

confidence: 99%

Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

Aminbaghai

Muŕın

Balduzzi

et al. 2017

Engineering Structures

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“…Plots of the dependence of the 1st eigenfrequency on the order n of the polynomial describing the longitudinal variation of the material properties are shown in Fig. 12 As shown in Table 6 and Fig. 12, the ANSYS and ABAQUS solid finite elements produce consistent results, which were considered as benchmark solutions.…”

Section: Eigenfrequencies and Mode Shapes Of A Cantilever Beam With An I Crosssection With Longitudinally Varying Materials Propertiesmentioning

confidence: 99%

“…[8] is extended by taking geometrical nonlinearity into account, and in [11], the effect of rotary and warping inertia is considered. Nonlinear torsional vibrations of thin-walled beams, exhibiting primary and secondary warping, are investigated in [12]. A solution for the vibration of Timoshenko beams by the isogeometric approach is presented in [13].…”

Section: Introductionmentioning

confidence: 99%

Torsional warping eigenmodes of FGM beams with longitudinally varying material properties

Muŕın

Aminbaghai

Hrabovský

et al. 2018

Engineering Structures

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In this paper, the influence of torsional warping of thin-walled cross-sections of twisted Functionally Graded Material (FGM) beams with a longitudinal polynomial variation of the material properties on their eigenvibrations is investigated, considering the secondary deformations due to the angle of twist. The transfer relations needed for the transfer matrix method are derived. Based on them, the local finite element equations of the twisted FGM beam are established. The warping part of the first derivative of the twist angle, caused by the bimoment, is considered as an additional degree of freedom at the beam nodes. The focus of the numerical

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“…[7] is extended taking the geometrical nonlinearity into account, and in [10], the effect of rotary and warping inertia is implemented. In [11], the nonlinear torsional vibrations of thin-walled beams exhibiting primary and secondary warping are investigated. In [12], a solution for the vibrations of Timoshenko beams by the isogeometric approach is presented, but warping effects are not considered.…”

Section: Introductionmentioning

confidence: 99%

Modelling of Warping Eigenvibration by Non-Uniform Torsion

Muŕın¹,

Aminbaghai²,

Hrabovský³

et al. 2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. This contribution contains a novel investigation of the influence of warping of the cross-section of twisted beams on their eigenvibrations. The investigation is based on the analogy of the bending beam theory and the non-uniform torsion theory of thin-walled open INTRODUCTIONBeam structures are often exposed to time-dependent loads. Commercial FEM codes allow performing modal and transient dynamic analysis by 3D beam finite elements with and without consideration of the warping effect. Very often the improved Saint-Venant theory of torsion is used and special mass matrices are proposed. Mostly, the bicurvature is chosen as an additional warping degree of freedom and the secondary torsion moment deformation effect (STMDE) is not considered.For example in [1], the beam element can be used with a lumped or a consistent mass matrix. The consistent mass matrix includes warping effects but does not include the effect of shear deformation. For the standard beam element, the consistent mass matrix is based on reference [2] with the exception that there are additional terms arising from the warping constant  I . For the warping element, lumped masses for the warping degree of freedom (bicurvature) are defined [3]. As stated in [1], for solid and closed thin-walled sections, the standard beam element can be used without significant error. However, for the open thinwalled sections, the warping beam element should be used. In [4], the warping beam finite element is recommended to be used only for open thin walled section beams. In [5], the finite beam element is implemented with unrestrained or restrained warping (BEAM188). In [6], the warping beam finite element can be used only for elastostatic analysis of straight beams. It should be noted that in technical practice as well as in the Eurocodes 3 (EC3) the effect of non-uniform torsion by the steel beams with closed cross-sections is not considered.In the most recent literature relatively little information can be found that refers to the solution for free and forced torsional vibration of beams with hollow cross-sections that include non-uniform torsion effects. In [7], a boundary element method is developed for the nonuniform torsional vibration problem of doubly symmetric composite bars of arbitrary variable cross-section. Dynamic analysis of 3-D beam elements, restrained at their edges, subjected to arbitrarily distributed dynamic loading, is presented in [8]. In [9], Ref. [7] is extended taking the geometrical nonlinearity into account, and in [10], the effect of rotary and warping inertia is implemented. In [11], the nonlinear torsional vibrations of thin-walled beams exhibiting primary and secondary warping are investigated. In [12], a solution for the vibrations of Timoshenko beams by the isogeometric approach is presented, but warping effects are not considered. In [13], geometrically non-linear free and forced vibrations of beams with non-symmetrical cross sections are investigated by the Saint-Venant theory of torsion. In [14], an axial-torsional vi...

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Nonlinear free vibrations of thin-walled beams in torsion

Cited by 17 publications

References 23 publications

Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

Torsional warping eigenmodes of FGM beams with longitudinally varying material properties

Modelling of Warping Eigenvibration by Non-Uniform Torsion

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