Stability of rotating shafts in a weak formulation

The stability analysis method is developed for a thin-walled rotating shaft with relaxed assumptions imposed on solutions. The problem is motivated by structural vibrations with external time-dependent parametric excitations which are controlled using surface mounted or embedded actuators and sensors. The commonly used strong form of dynamics equations involves irregularities which lead to computational difficulties for estimation and control problems. In order to avoid irregular terms resulting from differentiation of torques the dynamics equations are written in a weak form. The study of stability analysis is based on examining properties of Liapunov functional along a weak solution. Solving the problem is presented for an arbitrary combination of simply supported and clamped boundary conditions. Formulas defining dynamic stability regions are written explicitly.