On the dynamic stability of a cantilever under tangential follower force according to Timoshenko beam theory

Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Block 4, 1113 Sofia, Bulgaria
Journal of Sound and Vibration (Impact Factor: 1.86). 04/2008; 311:1431-1437. DOI: 10.1016/j.jsv.2007.10.005

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.

Download full-text


Available from: Vassil M. Vassilev, Jun 19, 2015
1 Follower
  • Source
    [Show abstract] [Hide abstract]
    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
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper a free-free uniform beam with damping effects subjected to follower and transversal forces at its end is considered as a model for a space structure. The effect of damping on the stability of the system is first investigated and the effects of the follower and transversal forces on the vibration of the beam are shown next. Proportional damping model is used in this work, hence, the effects of both internal (material) and external (viscous fluid) damping on the system are noted. In order to derive the frequency of the system, the Ritz method has been used. The mode shapes of the system must therefore be extracted. The Newmark method is utilized in the study of the system vibration. The results show that an increase in the follower and transversal forces leads to an increase of the vibrational motion of the beam which is not desirable.
    Structural Engineering & Mechanics 12/2009; 33(6). DOI:10.12989/sem.2009.33.6.709 · 0.80 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Flexible behaviors in new aerospace structures can lead to a degradation of their control and guidance system and undesired performance. The objectives of the current work are to analyze the vibration resulting from the propulsion force on a Single Stage to Orbit (SSTO) launch vehicle (LV). This is modeled as a follower force on a free-free Euler-Bernoulli beam consisting of two concentrated masses at the two free ends. Once the effects on the oscillation of the actuators are studied, a solution to reduce these oscillations will also be developed. To pursue this goal, the stability of the beam model is studied using Ritz method. It is determined that the transverse and rotary inertia of the concentrated masses cause a change in the critical follower force. A new dynamic model and an adaptive control system for an SSTO LV have been developed that allow the aerospace structure to run on its maximum bearable propulsion force with the optimum effects on the oscillation of its actuators. Simulation results show that such a control model provides an effective way to reduce the undesirable oscillations of the actuators.
    Structural Engineering & Mechanics 07/2013; 47(2). DOI:10.12989/sem.2013.47.2.149 · 0.80 Impact Factor