• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.695-700
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• 2000

The dynamic stability of spinning beam with free boundary conditions for both edges subjected to a tip follower force $P_0+P_1cos{\Omega}t$ is analyzed. It is studied that the beam has a concentrated mass. and then the effects of the axial locations of the mass are studied. The beam is modelled with the Timoshenko type shear deformations. The Hamilton's principle is used to derive the equations of motion, and the critical spinning speed of a beam subjected to a follower force with various non-dimensional parameters is investigated. The finite elements are used with $C^0$ continuity to analyze the spinning beam model, and the method of multiple scales is tried to investigate the dynamic instability regions. The governing equations of motion involve periodic coefficients, which are not in the form of standard Mathieu-Hill equations. The result shows that the concentrated mass increases the dynamic stability of the spinning free-free beam subjected to a thrust.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.9
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• pp.1385-1391
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• 1997

An analysis is presented on the stability of an elastic cantilever column subjected to a concentrated follower force as to the influence of the elastic restraint and a tip mass at the free end. The elastic restraint is formed by the rotatory springs. For this purpose, the governing equations and boundary conditions are derived by using Hamilton's principle, and the critical flutter loads and frequencies are obtained from the numerical evaluation of the eigenvalue functions of the considered system.

• Transactions of the Korean Society of Mechanical Engineers
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• v.5 no.4
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• pp.293-302
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• 1981

In this paper, the stability of a flexible missle, idealized as a free-free beam, is evaluated by using the finite element method. For the study, heavy machinery part is modeled as a concentrated mass and the thrust, which is controlled by a feedback sensor located at a predetermined position, is considered as a constant follower force. The aerodynamic forces, the structural damping, the cross sectional variation servo lag effect are neglected in this study. With unconstrained variational principle, the finite element method is applied to the nondimensionalized beam eqution. The matrix eigenvalue equation is obtained and the eigenvalues are calculated by a computer for the stability analysis. The stability is evaluated by the inspection of the eigenvalues are calculated by a computer for the stabilith analysis. The stabilith is evaluated by the inspection of the eigenvalues of the problem. For the study, the behaviors of the eigenvalues at various thrusts and the effects of the magnitudes and positions of the concentrated mass and directional control constant are analyzed.