Analysis of transverse oscillations of drilling rig derrick as Timoshenko beam with variable parameters along the length

Free and forced transverse oscillations of a drilling rig tower are considered. The computational model is represented as a Timoshenko beam with variable bending stiffness, running mass, and longitudinal force along the length. It is assumed that the tower is mounted on a rigid platform supported by an elastic base. Additionally, the tower is connected to the base by means of elastic braces. The crown block and rig service platforms attached to the tower are treated as rigid bodies. For the case of harmonic oscillations of a Timoshenko beam with variable parameters along its length, the differential equations of the amplitude functions are obtained and reduced to Volterra integral equations. Oscillations of a multi-span structure are calculated using the matrix method of initial parameters. An analysis of the results of calculations of transverse oscillations of a drill tower is presented.