The Timoshenko beam with strain rate damping supported by an elastic foundation

The development of the governing equations for a Timoshenko beam with strain rate damping is presented. Also presented are the governing differential equations for the Shear, Rayleigh and Bernoulli-Euler beams with strain rate damping. The Timoshenko beam with strain rate damping was assumed to be supported by a Winkler-type foundation and subjected to a point load moving with constant velocity. Roots of the steady-state equation are presented as functions of strain rate damping, foundation damping and moving load velocity. The steady-state response of the Rayleigh beam to the moving load is presented for various values of strain rate damping, foundation damping and moving load velocities.