Vibration and Stability of an Axially Moving Beam on Elastic Foundation

The free vibration of an axially moving elastic beam on simple supports resting on elastic foundation is investigated in this paper. Analytical expressions are derived by considering the ordinary differential equations obtained by the Galerkin truncation method. Critical axially moving velocity is computed for different foundation and supporting conditions. The phenomena of divergence and flutter are found beyond the critical velocity. The stability in the vicinity of critical state is studied and instability regions are discussed accounting for the parameters of axial tension and the foundation stiffness. The complex natural frequencies of the system are obtained by considering the governing partial differential equation without truncation. Some numerical examples are presented to illustrate the contributions of axial speed, tension, and the foundation stiffness.