Dynamic response of a Timoshenko beam to a continuous distributed moving load

In the paper we study dynamic response of a finite, simply supported Timoshenko beam subject to a moving continuously distributed forces. Three problems have been considered. The dynamic response of the Timoshenko beam under a uniform distributed load moving with a constant velocity v has been considered as the first problem. Obtained solutions allow to find the response of the beam under the interval of the finite length a uniformly distributed moving load. Part of the solutions are presented in a closed form instead of an infinite series. As the second problem the steady-state vibrations of the beam under uniformly distributed mass m1 moving with the constant velocity has been considered. The vibrations of the beam caused by the interval of the finite length randomly distributed load moving with constant velocity is considered as the last problem. It is assumed that load process is space-time stationary stochastic process.