Abstract
This paper presents the calculation of vibration of the cranes during moving loads when both the main beam and the trolley move simultaneously. There, Including the weight of the suspension hook - pully. The first oscillation model was proposed; the formulation of dynamic equations for this model is done by the Lagrange method. We will obtain a system of ordinary differential equations and partial derivative differential equations. Solving the system of differential equations is done by numerical methods. The results obtained are the oscillation of load and oscillation of suspension hook - pully during the operation of the cranes.