This paper studies the vibration of a truss structure composed of a number of rigidly connected Timoshenko beams. The excitation is provided by a moving oscillator of an unsprung mass that supports another mass through a spring (oscillator) and moves on top of the truss structure. Each component beam of the structure is meshed with a number of Timoshenko beam elements. The finite-element (FE) modes of the whole structure are first obtained for the nodes of the FE mesh and then they are converted into an analytical form that is constructed over all the elements of the top deck of the truss through the element shape functions, whereby the location of the moving oscillator is easily tracked and the displacement continuity and force equilibrium conditions at the contact point can be easily implemented. This numerical-analytical combined approach has the advantage of the versatility of the FE method in dealing with structures (trusses or frames in this paper) of arbitrary configurations and the special efficiency and convenience of the analytical method in dealing with moving loads. Vibration of the truss structure and vibration of the oscillator are studied through simulated examples. It is found that the dynamic response can be several times higher than the relevant static response at high speeds. It is also found that the dynamic contact force can be much higher than its static value and may become negative if the contact between the oscillator and the truss is assumed to be constantly maintained. Interestingly, suitably chosen parameter values can bring the dynamic response and the dynamic contact force close to their respective static values.