ON A VARIATIONAL PRINCIPLE IN THE THEORY OF DYNAMIC STABILITY OF ELASTIC-SYSTEMS

The main problem of the dynamic of an elastic system is to determine the boundary dividing the stable and unstable regions. This problem seems to be overlooked in the recent development of finite element methods. A variational principle is proposed for the critical parameter which determines the boundary dividing the stable and unstable regions. The proposed functional for the parameter has the classical form of a quotient. By this principle, many finite element methods may be borrowed simply for the numerical solution of various dynamic stability problems.