Discrete model of vibration of truck crane telescopic boom with consideration of the hydraulic cylinder of crane radius change in the rotary plane

In this paper the one degree of freedom discrete model representing the vibration of the telescopic boom of truck crane in the rotary plane has been presented. In the model the influence of the hydraulic cylinder of crane radius change has been considered. The formulation and solution of the problem has been based on the Lagrange multiplier formalism. The mathematical relations describing the equivalent mass and spring stiffness of the discrete model have been derived. The mathematical formulation is completed by the exemplary numerical results.