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Effects of Support Flexibility on the Stability of a Beam under a Follower Thrust and Inertia.

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The stability behavior of a slender structure, modeled by a beam, subjected to a follower force at one end and restrained at the other, is studied in detail in this paper. Denoting rigidities of lateral deflection and of rotation by alpha sub 1 and alpha sub 2 respectively, eigenvalue curves which dictate the stability behavior are plotted for several combinations of parameters alpha sub 1, alpha sub 2 and the magnitude of the thrust. Specifically, the critical loads prior to flutter instability are obtained for the three extreme cases alpha sub 1 infinity, alpha sub 2 infinity, alpha sub 1 infinity, alpha sub 2 0 and alpha sub 1 0, alpha sub 2 infinity, together with the case alpha sub 1 0, alpha sub 2 0 which is unstable at any load due to divergence mode as reported previously. Given a fixed magnitude of thrust, a region of stability or instability can be established in terms of support flexibilities. The increase of rigidity alpha sub 1 or alpha sub 2 can be stabilizing in one situation and destabilizing in another depending on the amount of the thrust and the relative magnitude of alpha sub 1 and alpha sub 2. These conclusions are illustrated in several sets of curves of various typical combinations of parameters. Author

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  • Structural Engineering and Building Technology
  • Mechanics

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