Transverse vibration of an uniform Euler–Bernoulli beam under linearly varying axial force

Naguleswaran, S.

doi:10.1016/s0022-460x(03)00741-7

Cited by 61 publications

(48 citation statements)

References 9 publications

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“…Instability is for all lengths of the divergence type. On the same figure are shown computations from [13] and [18], for intermediate values of the length. In [18], the static instability of a towed beam has been considered, which yields equations similar to that used here.…”

Section: B Effect Of Lengthmentioning

confidence: 99%

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Langre

Doaré

2015

J. Mech. Mater. Struct.

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The linear instability of a beam tensioned by its own weight is considered. It is shown that for long beams, in the sense of an adequate dimensionless parameter, the characteristics of the instability caused by a follower force do not depend on the length. The asymptotic regime significantly differs from that of short beams: flutter prevails for all types of follower loads, and flutter is localized at the edge of the beam. An approximate solution using matched assymptotic expansion is proposed for the case of a semi-infinite beam. Using a local criterion based on the stability of waves, the characteristics of this regime as well as its range of application can be well predicted. These results are finally discussed in relation with cases of flow-induced instabilities of slender structures.

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Section: B Effect Of Lengthmentioning

confidence: 99%

Untitled

Langre

Doaré

2015

J. Mech. Mater. Struct.

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“…(5) contains a differential equation with variable coefficients. A closed-form solution for this problem can be obtained through the Frobenius method by expressing the eigenvectors in terms of power series [19]. Appendix A reports the application of the Frobenius method to the specific problem analyzed, in the case of uniform distributed mass and stiffness through the pier length.…”

Section: Eigenvalue Problem Solutionmentioning

confidence: 99%

“…It is noted that the eigenvalue problem that needs to be solved to determine the vibration modes of the systems involves a differential equation with variable coefficients. The solution of this problem is obtained by extending previous formulations and results for similar problems [2,[18][19][20][21], in particular by application of the Frobenius method [19].…”

Section: Introductionmentioning

confidence: 99%

An Analytical Technique for the Seismic Response Assessment of Slender Bridge Piers

Tubaldi¹,

Tassotti²,

Dall’Asta³

et al. 2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. This work proposes an analytical technique for the analysis of the effects of axial loads on the dynamic behaviour and seismic response of tall and slender bridge piers. The pier is modeled as a linear elastic INTRODUCTIONA large number of bridges over mountain areas and deep valleys are built on tall piers. Because of the rugged topography of these areas, the height of bridge piers could even reach 200 m. The seismic assessment and design of slender piers usually differs from that of short piers because of the influence of axial load effects on the dynamic behaviour.It is well known that axial load effects induce in general a reduction of the transverse bending stiffness and this may have different consequences on the transverse structural response depending on the type of loading experienced by the system. In the case of static loadings, the axial load effects usually increase the response beyond the values obtained by first order analysis. On the other hand, in the case of dynamic loadings such as earthquake-induced loadings, the interaction between axial loads and transverse displacements induces changes in the system dynamic properties and elastic periods elongation [1,2], which in turn may result on either a decrease or an increase of displacements and internal action demands.In bridge engineering-design practice, the axial-load effects are usually taken into account in a simplified manner by introducing an amplification factor for the piers seismic moments [3] evaluated via first-order analysis. Many studies in past years have been devoted to the calibration of expressions for the amplification factor [1,[4][5][6][7][8][9], on the basis of simple singledegree-of-freedom (SDOF) models. These models often consisted in a rigid inverted pendulum with an elasto-plastic rotational restraint at the base, and a tip mass at the free end with a concentrated weight force. Recent works [10,11] extended the application of the amplification factor method also to the direct displacement based design of bridge piers. Other alternative methods were defined to account for axial load effects in a simplified way, without recourse to the amplification factor. In this context, the method proposed in [12] introduced the concepts of effective height and yield point spectra for the design of piers behaving as SDOF system. The main limitation of the SDOF model employed in these studies is that it is adequate to represent only short bridge piers, for which the inertia is concentrated at the top whereas the distributed pier mass and the relevant variation of axial loads can be neglected. Slender piers, as those considered in this study, are on the contrary characterized by significant distributed masses and the analysis of their dynamic behavior should also consider higher modes effects [13]. Only few studies analyzed the axial-load effects on slender piers by employing refined multi-degree-of-freedom (MDOF) models. In this context are the work of [14] and [15], analyzing the evolution of plastic hinges formation in tall p...

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“…2 Regarding uniform Euler-Bernoulli beams under linearly varying fully tensile, the structure natural frequencies may be increased or decreased, and parameters change the forbidden frequencies of the mechanical system, considering the pre-stress force. 3 The influence of temperature was also determined by specifying the arbitrary high temperature on the outer surface and the ambient temperature on the inner surface of cylindrical shells. In this case, the prestressed state was induced by thermal loading.…”

Section: Introductionmentioning

confidence: 99%

Acoustic Characteristic Analysis of Prestressed Cylindrical Shells in Local Areas

Chen¹,

Liu²

2016

IJAV

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The influence of prestress on dynamic responses and acoustic radiation for thin cylindrical shells is analyzed in this study. The strain-displacement equation of cylindrical shells with prestress in local areas is established based on the Flügge theory. The structural-acoustic radiation formulation for prestressed cylindrical shells in local areas is instituted by using the variational principle. A numerical analysis is then carried out. The numerical results are validated by comparing the influence of prestress on acoustic radiation power and directivity. This study shows that prestress significantly affects the dynamic characteristics of cylindrical shells.

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Transverse vibration of an uniform Euler–Bernoulli beam under linearly varying axial force

Cited by 61 publications

References 9 publications

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An Analytical Technique for the Seismic Response Assessment of Slender Bridge Piers

Acoustic Characteristic Analysis of Prestressed Cylindrical Shells in Local Areas

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