The influence of damping on the dynamic stability of complex mechanical systems, as exemplified by a truck crane

Abstract

This work aimed to model and analyze the dynamic stability of a truck crane boom change system, taking into account the effect of various types of vibration damping on its dynamic stability. The paper formulates and solves boundary-value problems for a truck crane boom change system, accounting for damping, using a real DST0285 truck crane boom change system modeled as Bernoulli-Euler beams and selected discrete elements. Using Hamilton’s variational principle, the equation of motion of the system was obtained, and, taking into account geometric and continuity conditions, the natural boundary conditions were determined. The equation of motion was then transformed into the Mathieu equation, whose parameters allowed the determination of the system’s stable solution range.