Influence of support clamping on the dynamic stability of an elastic rod

Zorii, L. M.; Chernukha, Yu. A.

doi:10.1007/bf00885991

Cited by 2 publications

(3 citation statements)

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“…Intuitively, for 𝑎𝑎 → 0 one should find the results already obtained in [1], while for 𝑎𝑎 → 𝑙𝑙 one should find again the Eulerian critical load. This implies (as indeed already pointed out in [4] and later in [5]) that there should exist a transition value 𝑎𝑎 = 𝑎𝑎 * such that when 𝑎𝑎 < 𝑎𝑎 * there is instability by divergence at infinity, while for 𝑎𝑎 > 𝑎𝑎 * there is Eulerian instability by divergence. Other lumped mass systems have been studied (Fig.…”

Section: Introductionsupporting

confidence: 65%

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On the dynamic stability of elastic structures subjected to follower forces

Levi

2023

Theoretical and Applied Mechanics - AIMETA 2022

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Abstract. Within the framework of the second-order theory, some classical stability problems, whose critical load corresponded to dynamic instability, were considered in the paper [1]. The main focus was on systems with just one lumped mass. This idealization, together with the assumption of negligible axial strain and the adoption of the second-order theory, reduced the considered systems to a single Lagrangian coordinate. In this way, static methods could be applied to derive the analytical expression of the stiffness coefficient and to study the dynamic stability, starting with a well-known example, namely, a cantilever beam with a lumped mass at the free end subjected to a follower load [2]. In this paper, a new lumped mass system is studied: a straight-axis beam with constant cross-sectional area and stiffness, mass-free, hinged at one end, simply supported at an intermediate point (with a sliding plane parallel to the beam axis) and with the other end free, where a lumped mass is present and a follower force is applied. As in the examples shown in [1], in this example the first asymptote of the stiffness coefficient corresponds to the critical load, due to divergence at infinity. It is shown that this critical load is equal to the buckling load due to divergence of an auxiliary structure, which differs from the original one in that the concentrated mass is replaced by a constraint that blocks the corresponding Lagrangian coordinate.

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Section: Introductionsupporting

confidence: 65%

“…2a). In the case of uniformly distributed mass, the system was studied by Zorii and Chernukha [4] and later by Elishakoff and Hollkamp [5].…”

Section: Introductionmentioning

confidence: 99%

On the dynamic stability of elastic structures subjected to follower forces

Levi

2023

Theoretical and Applied Mechanics - AIMETA 2022

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“…Vibration analysis is important part in the dynamic optimization design of professor Wen. So vibration analysis need exist in engineering design, the model of double-span beam applies to train track, bridge, wall column and so on [1][2][3][4][5][6].Vibration analysis of dynamic characteristic can reference method to many complex bodies the middle simply supported beam is studied by transfer matrix method in this paper. Calculate the natural frequencies and instability critical pressure.…”

Section: Introductionmentioning

confidence: 99%

Research on Vibration and Instability of the Double-Span Beam Base on Transfer Matrix

Liu

Feng

Chen

et al. 2009

AMM

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The vibration and instability of a beam which is Double-span Euler Beam with axial force is studied by transfer matrix method. The transfer matrix of transverse free vibration and axial compression of the beam is derived. Then based on the assembled transferring matrix, the effect of the position of intermediate support on the natural frequencies and Euler critical axial force of the beam is discussed, which offered a useful method to start research of vibration of complicated framework.

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Influence of support clamping on the dynamic stability of an elastic rod

Cited by 2 publications

References 0 publications

On the dynamic stability of elastic structures subjected to follower forces

On the dynamic stability of elastic structures subjected to follower forces

Research on Vibration and Instability of the Double-Span Beam Base on Transfer Matrix

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