The influence of tip mass offset on the stability of Beck's column

In this paper, the stability of a slender cantilever carrying a tip mass at its free end and subjected there to a follower force is investigated. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The associated boundary value problem is solved and the exact frequency equation is derived. The frequency equation is solved numerically for the case in which both the beam and the tip mass have circular cross-sections. The numerical computations indicate that the system loses stability only through flutter. The variation of the values of the critical flutter load Q_cr with the tip mass offset parameter ξ is shown graphically for four values of the tip mass density to beam density ratio p. These calculations reveal that, at sufficiently small values of ξ, Q_cr decreases sharply for increasing values of p. For values of ξ sufficiently large, however, the situation is reversed as the value of Q_cr increases with increasing p.