• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.7 s.124
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• pp.605-610
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• 2007

In this paper a dynamic behavior(natural frequency) of a cracked cantilever beam subjected to follower force is presented. In addition, an analysis of the flutter and buckling instability of a cracked cantilever beam subjected to a follower compressive load is presented. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The vibration analysis on such cracked beam is conducted to identify the critical follower force for flutter instability based on the variation of the first two resonant frequencies of the beam. Besides, the effect of the crack's intensity and location on the flutter follower force is studied. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

• Structural Engineering and Mechanics
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• v.16 no.2
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• pp.195-217
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• 2003

This paper, which is an extension of a previous work by Viola et al. (2002), deals with the dynamic stability of beams under a triangularly distributed sub-tangential forces when the effect of an elastically restrained end is taken into account. The sub-tangential forces can be realised by a combination of axial and tangential follower forces, that are conservative and non-conservative forces, respectively. The studied beams become unstable in the form of either flutter or divergence, depending on the degree of non-conservativeness of the distributed sub-tangential forces and the stiffness of the elastically restrained end. A non-conservative parameter ${\alpha}$ is introduced to provide all possible combinations of these forces. Problems of this kind are usually, at least in the first approximation, reduced to the analysis of beams according to the Bernoulli-Euler theory if shear deformability and rotational inertia are negligible. The equation governing the system may be derived from the extended form of Hamilton's principle. The stability maps will be obtained from the eigenvalue analysis in order to define the divergence and flutter domain. The passage from divergence to flutter is associated with a noticeable lowering of the critical load. A number of particular cases can be immediately recovered.

• Transactions of the Korean Society of Mechanical Engineers
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• v.8 no.2
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• pp.119-126
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• 1984

An analysis is presented for the vibration and stability of Beck's column carring a tip mass at its free and subjected there to a follower compressive force by using variational approach. The influence of transverse shear deformation and rotatory inertial of the mass of the column upon the critical flutter load and frequency is considered, and Timoshenko's shear coefficient K' is calculated by Cowper's formulae. It is, moreover, worth noticing that the influence of inertial moment of tip mass upon the flutter load and frequency is investigated. The centroid of a tip mass is offset from the free end of the beam and located along its extended axis of the two cases, one of which has a tip mass increasing as .xi., the tip mass offset parameter, is augmented, the other has a tip mass constant but the inertial moment is variable according to a magnitude of .eta., the tip mass offset parament. This study reveals that the effects of inertial moment of a tip mass and larger value of P are specially remarkable even a tip mass is a same.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.3
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• pp.57-65
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• 1990

The finite element menthod for the investigation of the static and dynamic stability of the plane framed structures subjected to non-conservative forces is presented. By using the Hermitian polynomial as the shape function, the geometric stiffness matrix, the load correction stiffness matrix for non-conservative forces, and the matrix equation of internal and external damping are derived. Then, a matrix equation of the motion for the non-conservative system is formulated and the critical divergence and flutter loads are determined from this equation.