Many researchers have carried out research on beam vibrations with different shapes, but in many cases their study is limited to a straight beam. However curved beams are widely used in space and traortation industries. In this type of beams, in addition to the radial displacement and rotation, there is also a tangential displacement. Free and forced vibration analysis of a circularly curved Timoshenko beam with uniform cross section which is both the rotary inertia and shear deformation are considered, is study. The differential transform method, DTM and differential quadratic method, DQM, as effective mathematical methods, are used to calculate the natural frequencies and the mode shapes. The system force response is assessed for a moving concentrated load and mass with a constant speed, respectively. The moving mass may be regarded as the Coriolis effect, centrifugal, gravitational and inertia forces generated by forces moving along a curved beam, which were rarely studied by previous researchers. For obtaining the forced vibration response of the system, the same time functions (STF) method is utilized and the orthogonality conditions, derived in this paper, have been set out. The differences between responses of the system are analyzed by applying moving load and moving mass. A numerical example is solved. It can be seen that when the mass moving on a curved beam, by increasing the radius of curvature with constant length of the curved beam, increases the radial displacement of the midpoint of that in the direction of the effect of the weight force. The effect of the velocity and mass when the mass moving on the curved beam, was studied. It was observed that at low speeds and heavy masses, the behavior of the curved beam in the moving mass and the moving load is approximately the same. Finally, the critical speeds which caused the resonance phenomena were calculated. Keywords: Vibration analysis; Moving ma Moving load; Circularly curved Timoshenko beam; Resonance;
