stability criterion using Hamilton’s principle and the Bernoulli-Euler theory. The stiffness of the guide and sealing elements between successive stages of the hydraulic cylinder were considered in this paper. These stiffnesses were modelled using translational and rotational springs. The effects of cylinder wall thickness, piston rod diameter, and thickness of guiding and sealing elements on the natural vibration of the system were analysed. Results are presented in the form of characteristic curves on the plane load – natural frequency with different parameters characterizing the considered hydraulic cylinder.

application point is located at different heights between the upper and lower supports. In addition, the longitudinal displacement and rotation of both of the system ends are limited by the discrete elements in the form of translational and rotational springs. This nonlinear system is based on the screw drive used in the vertical lift platform for disabled people or cargo lift equipped with an engine room located in the lower part of the frame. The boundary problem of free vibrations of the mentioned system has been formulated on the basis of Bernoulli - Euler theory and due to nonlinear expressions the solution of the problem was conducted with small parameter method. The results of numerical simulations are concern on linear and nonlinear component of vibrations in relation to the location of external load application and influence of asymmetric value of supports stiffness on the free vibration frequency.

Method. Averaged distribution of material properties is obtained in individual segments of the column in subsequent heating times. The mathematical model of free vibrations takes into account the thermal expansion of the material and the effect of changing the Young's modulus resulting from the effect of heat load. The boundary problem of the free vibrations of the considered system is limited to the linear range (the linear component of natural frequency is considered). The influence of the heat source exposure time on the course of characteristic curves (on the plane: load – natural frequency) is determined. The results are presented for various column diameters.

strength of cylinder barrels (material effort) were included due to analysis. Boundary value problem concerning the stability of the system was formulated on the basis of the static stability criterion. Lame’s theory for thick pipes were used for determination of destructive load from the viewpoint of the material effort. Numerical simulations were performed. The results specifying the influence of mounting rigidity on stability and strength of cylinder barrels were presented by using non-dimensional parameters.

results of numerical simulations concern the first vibration frequency (linear and non-linear components) in relation to the location and magnitude of external load application and different rotational spring stiffness. This nonlinear system is based on the screw drive used in the newly designed vertical platform lifts.