Torsional warping eigenmodes including the effect of the secondary torsion moment on the deformations

Aminbaghai, Mehdi; Muŕın, Just́ın; Hrabovský, Juraj; Mang, Herbert A.

doi:10.1016/j.engstruct.2015.10.022

Cited by 27 publications

(22 citation statements)

References 35 publications

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“…[1]). Equation (1) represents the mathematical formulation of the second-order torsional warping theory with consideration of the secondary torsionmoment deformation-effect (e.g.…”

Section: Equations Of Nonuniform Torsion With Efect Of Stmde and Varimentioning

confidence: 99%

“…The circular natural frequencies j ω , j , , , 1 2 follow from the zeros of the determinant of the reduced system of equations. An iterative method was used to find these zeros [1]. The natural frequencies j j f / ω 2 , j , , , 1 2 are computed subsequently.…”

Section: Torsional Modal Analyses Of a Beam With I Cross-section Submentioning

confidence: 99%

“…On the other hand, the influence of the STMDE by nonuniform elastostatic torsion of the open thin-walled sections is not significant. A broad comprehensive overview of the literature dealing with the issue of non-uniform torsion of thinwalled beams can be found, for example, in [1] and [2]. Thin-walled beam structures are frequently exposed to dynamic loads.…”

Section: Introductionmentioning

confidence: 99%

“…A common feature of the above cited articles is disregard of the effect of the variable axial force on torsional warping. In this paper, the work reported in [1] is extended to uniform and non-uniform torsional analysis of beams with a variable axial force. The differential equations of beams with such an axial force are formulated for Saint-Venant and non-uniform torsional deformations, including inertial line moments.…”

Section: Introductionmentioning

confidence: 99%

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Second-Order Torsional Warping Modal Analysis of Thin-Walled Beams

Muŕın¹,

Aminbaghai²,

Hrabovský³

et al. 2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…[1]). Equation (1) represents the mathematical formulation of the second-order torsional warping theory with consideration of the secondary torsionmoment deformation-effect (e.g.…”

Section: Equations Of Nonuniform Torsion With Efect Of Stmde and Varimentioning

confidence: 99%

Section: Torsional Modal Analyses Of a Beam With I Cross-section Submentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Second-Order Torsional Warping Modal Analysis of Thin-Walled Beams

Muŕın¹,

Aminbaghai²,

Hrabovský³

et al. 2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…The chosen material characteristics and the cross-sectional parameters are listed in Tables 3 and 5. The boundary conditions are the same as in section 3.1, expressions (20) and (21). In the following, the cross-sectional parameters and the cross-sectional characteristics are calculated by ANSYS [4] and [23] for t = 5 mm and t = 10 mm:…”

Section: Warping Eigenfrequencies and Mode Shapes Of A Cantilever Recmentioning

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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