A hydraulic cylinder subjected to Eulerʹs load in aspect of the stability and free vibrations taking into account discrete elastic elements

Theoretical and numerical research into the stability and free vibrations of a slender system in the form of a hydraulic cylinder subjected to Eulerʹs load was carried out in this paper. The rigidities in the constructional nods realising the load of the considered system were taken into account in the system. Both rotational and translational springs were applied to the loading nods. Regions of the flexural rigidity asymmetry factor for the piston rod and cylinder, where the system is subject to damage as a result of stability loss, were determined in the frame of numerical research into the hydraulic cylinder. In this paper critical load and characteristic curves were also determined in the plane: load–natural frequency. These two quantities were determined for different parameters of the system: the flexural rigidity asymmetry factor for the piston rod and cylinder, the degree of coverage of cylinder, the rigidities of the rotational and translational springs, and the total rigidity factor of the system.