On the dynamic stability of a cantilever under tangential follower force according to Timoshenko beam theory
ABSTRACT The dynamic stability of a cantilevered Timoshenko beam lying on an elastic foundation of Winkler type and subjected to a tangential follower force is studied. Two models describing this phenomenon are examined and their predictions are compared in several special cases. For the values of the beam parameters considered here, the critical compressive forces obtained using these models differ substantially only for short beams as has already been established in other cases. Both models are found to predict dynamic instability of cantilevers under tension unlike the Bernoulli–Euler beam theory. For a beam of intermediate slenderness the Winkler foundation is found to reduce the critical tensile force.
Full-textDOI: · Available from: Vassil M. Vassilev, Aug 13, 2015
- SourceAvailable from: Abdolrasoul Ranjbaran
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- "The changes in the dynamic characteristics, due to the presence of a crack on an axially loaded uniform Timoshenko beam, are investigated by Viola et al. . The dynamic stability of a cantilever Timoshenko beam on an elastic foundation of Winkler type and subjected to a follower force is studied by Djondjorov and Vassilev . The Winkler foundation is found to reduce the critical tensile force for a beam of intermediate slenderness. "
ABSTRACT: The dynamic stability of cracked beams under the axial and follower force is studied. The governing equation and the closed form solution for the dynamic stability interaction diagram are derived. Innovative and simple algebraic equations for the interaction diagram are proposed. Thanks to these equations for construction of a diagram only the coordinates of the key points on the load and frequency axes is needed. Through extensive numerical experiments the accuracy, efficiency and robustness of the work is verified.Scientia Iranica 04/2013; 20(1):57-64. DOI:10.1016/j.scient.2012.11.005 · 0.84 Impact Factor
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ABSTRACT: This paper deals with the problem of the instability regions of a free-free flexible jointed bipartite beam under the follower and transversal forces as a realistic simulation of a two-stage aerospace structure. The aim of this study is to analyze the effects of the characteristics of a flexible joint on the beam instability to use maximum bearable propulsion force. A parametric study is conducted to investigate the effects of the stiffness and the location of the joint on the critical follower force by the Ritz method and the Newmark method, then to research the vibrational properties of the structure. It has been shown that the nature of instability is quite unpredictable and dependent on the stiffness and the location of the joint. The increase of the follower force or the transversal force will increase the vibration of the model and consequently cause a destructive phenomenon in the control system of the aerospace structure. Furthermore, this paper introduces a new concept of the parametric approach to analyze the characteristics effects of a flexible two-stage aerospace structure joint design.Journal of Zhejiang University - Science A: Applied Physics & Engineering 09/2009; 10(9):1252-1262. DOI:10.1631/jzus.A0820621 · 0.61 Impact Factor
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ABSTRACT: Axial deformation is not involved in the formulation of linear buckling caused by axial force. Likewise, twisting is not present in linear buckling caused by axial torque. The dynamic axial–torsional buckling of structural frames in the presence of follower axial force will be solved by means of dynamic stiffness using power series. Variationally consistent natural boundary conditions are given so that the resulting dynamic stiffness is symmetrical for conservative loading. Some parts of the boundary forces disappeared for follower axial forces due to consistent tangency to the neutral axis. The deficiency of the power series method to deal with non-uniform sections is highlighted. New instability phenomena for a simple column are studied in detail. It is shown that columns can buckle under direct follower tension. Follower tension decreases the natural frequency initially and then increases it rapidly after a turning point. The first pair of modes about the major axis and that about the minor axis of a rectangular section column meet at one crossing point. A very small axial torque will change the crossing into flutter-like tongues. These tongues are common in compressive follower force. These tongues caused by axial torque are reported here for the first time.International Journal of Mechanical Sciences 11/2009; 51(11):807-815. DOI:10.1016/j.ijmecsci.2009.09.011 · 2.06 Impact Factor