Equilibrium solutions of axially moving Timoshenko beam with a supercritical speed

Abstract

Abstract Analytical solution of the equilibrium configuration of an axially moving Timoshenko beam in supercritical regime is studied. Three kinds of classical boundary conditions are considered. An analytical solution of the equilibrium configuration in terms of the axial velocity in supercritical regime is determined. But most of all, for an axially moving Timoshenko beam with the fixed ends in supercritical regime, an anti-symmetric configuration is firstly detected. And, its analytical solution is solved. Besides, numerical example shows that the solution of the equilibrium configuration bifurcates with axially velocity. And the critical velocity derived from the Timoshenko beam theory is smaller than that derived from Euler-Bernoulli beam theory. The amplitude of the solution of equilibrium configuration derived from Timoshenko beam is larger.