On the rotating rod with shear and extensibility

Stability of a heavy rotating rod is studied by energy method. The generalized constitutive equations are used so that both extensibility of the rod axis and the influence of the shear stresses are taken into account. It is shown that the total potential energy of the rod is not a minimum when the angular velocity posseses a value higher than the critical value determined from the linearized equilibrium equations. An estimate of the maximal deflection in the post-critical state is also obtained. Received: November 8, 1996