Slip-through of a heavy elastica on point supports

Abstract

a b s t r a c tIn this paper, we study the deformation and stability of a heavy elastica resting symmetrically on two frictionless point supports on the same horizontal level. The static analysis finds multiple equilibria when the distance of the two point supports is smaller than a certain value. In order to determine whether these equilibria are stable, a dynamic analysis is conducted to calculate their natural frequencies. In order to take into account the sliding between the elastica and the smooth point supports during vibration, a dynamic analysis based on an Eulerian description is adopted. It is found that stable equilibrium can exist only when the half support span a is between two limits a ðsÞ min and a ðsÞ max . This range depends on a dimensionless ratio between the weight density and the flexural rigidity of the elastica. When an a between a ðsÞ min and a ðsÞ max decreases and approaches a ðsÞ min , the elastica will slip away from the side. On the other hand, when an a between a ðsÞ min and a ðsÞ max increases and approaches a ðsÞ max , the elastica will slip through between the two supports.

Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection

“…Likewise, an elastica-type dynamic stability of viscoelastic columns with its behavior given in terms of the Boltzmann superposition principle was discussed by Suire and Cederbaum [25]. Moreover, the boundary conditions were also extended from the commonly used conditions, namely, simply supported and clamped-free conditions, to clamped-hinged condition [26], frictional end [27], and slippery support [28] conditions.…”

Large deformation and stability of an extensible elastica with an unknown length

“…The stability of a beam under a concentrated force, which is clamped at one end while sliding over a point support at the other, has been studied by Zhang and Yang (2005). The slip-through of a beam under self-weight resting on two point supports has been examined by Chen et al (2010). With the particular choice of boundary conditions in the present paper, the part of the beam in between the clamping devices is fully decoupled from the outside part without any idealizing assumptions being necessary, in contrast to those cases, in which the beam slides over a point support.…”

Instability of a constrained pendulum system

“…Static and dynamic analysis of cables is given by Irvine 9 and Tadjbakhsh and Wang. 10 Chen, Li and Ro 11 have conducted linear stability analysis of a heavy flexible beam that is resting on frictionless point supports. Their analysis is similar in nature to one that we do here.…”