Coupled bending and torsional vibration of axially loaded Bernoulli–Euler beams including warping effects

Li, Jun; Rongying, Shen; Hu, Hua; Xian-ding, Jin

doi:10.1016/j.apacoust.2003.07.006

Cited by 35 publications

(25 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Apart from the above, various coupled vibrational behaviors of beam structures, caused by different geometric [2][3][4][5][6][7][8][9][10] and material couplings [11][12][13][14][15][16][17][18][19][20], have also been thoroughly studied and their associated findings have been well established. The coupled vibrations and stability of axially loaded, or centrifugally stiffened, beam elements have also been investigated [21][22][23][24][25][26][27][28][29][30][31]. However, the literature on the effects of combined axial load and end moment and the couplings resulting from the end moment on the stability and vibration characteristics of beams are scarce [32][33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

“…The effects of warping have been neglected in this study. Jun et al [26] examined the coupled flexural-torsional vibration of an axially loaded thin walled beam with monosymmetrical cross sections by including effects of warping. The effect of axial load has also been previously studied by Murthy and Neogy [27] for clamped and pinned boundary conditions, as well as by Gellert and Gluck [28] for cantilevered boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Flexural-Torsional Vibration and Stability of Beams Subjected to Axial Load and End Moment

Kashani

Jayasinghe

Hashemi

2014

Shock and Vibration

View full text Add to dashboard Cite

The free vibration of beams, subjected to a constant axial load and end moment and various boundary conditions, is examined. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the differential equations governing coupled flexural-torsional vibrations and stability of a uniform, slender, isotropic, homogeneous, and linearly elastic beam, undergoing linear harmonic vibration, are first reviewed. The existing formulations are then briefly discussed and a conventional finite element method (FEM) is developed. Exploiting the MATLAB-based code, the resulting linear Eigenvalue problem is then solved to determine the Eigensolutions (i.e., natural frequencies and modes) of illustrative examples, exhibiting geometric bending-torsion coupling. Various classical boundary conditions are considered and the FEM frequency results are validated against those obtained from a commercial software (ANSYS) and the data available in the literature. Tensile axial force is found to increase natural frequencies, indicating beam stiffening. However, when a force and an end moment are acting in combination, the moment reduces the stiffness of the beam and the stiffness of the beam is found to be more sensitive to the changes in the magnitude of the axial force compared to the moment. A buckling analysis of the beam is also carried out to determine the critical buckling end moment and axial compressive force.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Flexural-Torsional Vibration and Stability of Beams Subjected to Axial Load and End Moment

Kashani

Jayasinghe

Hashemi

2014

Shock and Vibration

View full text Add to dashboard Cite

show abstract

“…Similarly, strain distribution in the whole space should be represented as a linear combination of their corresponding strain components of the entire sampling surfaces as (8).…”

Section: Application Of Sampling Surfacementioning

confidence: 99%

“…A variety of simplified 1D theories have been proposed so far, which are commonly divided into two aspects as follows: the classical beam theory (CBT) and the shear deformation beam theories (SDBTs). These specialties make them very attractive in the mechanics analysis of beams [2][3][4][5][6][7][8][9][10]. However, it is needed to be pointed out that the CBT is incapable of considering transverse deformation effect.…”

Section: Introductionmentioning

confidence: 99%

Effects of Transverse Deformation on Free Vibration of 2D Curved Beams with General Restraints

Wang

Miao

et al. 2017

Shock and Vibration

View full text Add to dashboard Cite

An efficient modified Fourier series-based sampling surface approach is proposed for the analytical evaluation of the vibration characteristics of thick curved beams subjected to general restraints. The theoretical models of the beams are formulated by the theory of elasticity in two dimensions, which allows arbitrary thickness configurations to be tackled. As an innovation of this work, the approach is based upon the sampling surface method combined with the use of modified Fourier series approximation. In particular, the transverse beam domain is discretized by a set of sampling surfaces with unequal spaces, and the displacement components in beam domain coinciding with these surfaces are mathematically described as a set of modified Fourier series in which certain supplementary functions are included to remove all the relevant discontinuities with the displacements and their derivatives at the boundaries to form a mathematically complete set and guarantee the results convergent to the exact solutions. The final results are numerically solved using a modified variational principle by means of Lagrange multipliers and penalty method for the sake of arbitrary boundary conditions. The influences of transverse normal and shear deformation on the vibration characteristics with respect to the geometrical dimension and boundary conditions are systematically evaluated.

show abstract

“…Jun et al [14] studied the dynamics of axially loaded thin-walled beams of open, mono-symmetrical section. The studies considered the effect of warping stiffness, but were restricted to Euler-Bernoulli beam theory and isotropic material only.…”

Section: Introductionmentioning

confidence: 99%

Equations of motion of rotating composite beam with a nonconstant rotation speed and an arbitrary preset angle

2014

View full text Add to dashboard Cite

In the presented paper the equations of motion of a rotating composite Timoshenko beam are derived by utilising the Hamilton principle. The nonclassical effects like material anisotropy, transverse shear and both primary and secondary cross-section warpings are taken into account in the analysis. As an extension of the other papers known to the authors a nonconstant rotating speed and an arbitrary beam's preset (pitch) angle are considered. It is shown that the resulting general equations of motion are coupled together and form a nonlinear system of PDEs. Two cases of an open and closed box-beam cross-section made of symmetric laminate are analysed in details. It is shown that considering different pitch angles there is a strong effect in coupling of flapwise bending with chordwise bending motions due to a centrifugal force. Moreover, a consequence of terms related to nonconstant rotating speed is presented. Therefore it is shown that both the variable rotating speed and nonzero pitch angle have significant impact on systems dynamics and need to be considered in modelling of rotating beams.

show abstract

Coupled bending and torsional vibration of axially loaded Bernoulli–Euler beams including warping effects

Cited by 35 publications

References 19 publications

On the Flexural-Torsional Vibration and Stability of Beams Subjected to Axial Load and End Moment

On the Flexural-Torsional Vibration and Stability of Beams Subjected to Axial Load and End Moment

Effects of Transverse Deformation on Free Vibration of 2D Curved Beams with General Restraints

Equations of motion of rotating composite beam with a nonconstant rotation speed and an arbitrary preset angle

Contact Info

Product

Resources

About