• Journal of the Korean Society for Precision Engineering
• /
• v.22 no.10 s.175
• /
• pp.65-71
• /
• 2005

This paper presents the dynamic stability of a cantilevered Timoshenko beam on partial elastic foundations subjected to a follower force. The beam with a tip concentrated mass is assumed to be a Timoshenko beam taking into account its rotary inertia and shear deformation. Governing equations are derived by extended Hamilton's principle, and finite element method is applied to solve the discretized equation. Critical follower force depending on the attachment ratios of partial elastic foundations, rotary inertia of the beam and magnitude and rotary inertia of the tip mass is fully investigated.

• Proceedings of the KSME Conference
• /
• 2004.04a
• /
• pp.911-916
• /
• 2004

The paper deals with the dynamic stability of a cantilevered Timoshenko beam on partial elastic foundations subjected to a follower force. The beam is assumed to be a Timoshenko beam with a concentrated mass taking into account its rotary inertia and shear deformation. Governing equations are derived by extended Hamilton's principle, and FEM is applied to solve the discretized equation. Critical follower force depending on the attachment ratios of partial elastic foundations, concentrated mass and rotary inertia of the beam is fully investigated.

• Journal of Mechanical Science and Technology
• /
• v.20 no.9
• /
• pp.1355-1360
• /
• 2006

This paper presents the dynamic stability of a cantilevered Timoshenko beam with a concentrated mass, partially attached to elastic foundations, and subjected to a follower force. Governing equations are derived from the extended Hamilton's principle, and FEM is applied to solve the discretized equation. The influence of some parameters such as the elastic foundation parameter, the positions of partial elastic foundations, shear deformations, the rotary inertia of the beam, and the mass and the rotary inertia of the concentrated mass on the critical flutter load is investigated. Finally, the optimal attachment ratio of partial elastic foundation that maximizes the critical flutter load is presented.