ON THE BUCKLING OF AN ELASTIC ROTATING BEAM

A nonlinear model is developed, which describes the buckling phenomena of an elastic beam clamped to the interior of a rotating wheel. We us e a power series method to obtain an approximate expression of the buc kling equation and compare this with previous results in the literatur e. The linearized problem is integrated and this results in a second o rder differential equation of the Fuchs type, which allows an asymptot ic expansion of the buckling equation. By means of Lyapunov and Chetae v functions, a rigorous proof is given that the loss of stability of t he trivial equilibrium shape occurs for any length of the beam provide d the angular velocity of the rotating wheel is sufficiently large. Fi nally we discuss the nonlinear problem and describe the qualitative be haviour of branches in a bifurcation diagram.