This study analytically and numerically modeled the dynamics of a gyroscopic rigid rotor with linear and nonlinear cubic damping and nonlinear cubic stiffness of an elastic support. It has been shown that (i) joint linear and nonlinear cubic damping significantly suppresses the vibration amplitude (including the maximum) in the resonant velocity region and beyond it, and (ii) joint linear and nonlinear cubic damping more effectively affects the boundaries of the bistability region by its narrowing than linear damping. A methodology is proposed for determining and identifying the coefficients of nonlinear stiffness, linear damping, and nonlinear cubic damping of the support material, where jump-like effects are eliminated. Damping also affects the stability of motion; if linear damping shifts the left boundary of the instability region towards large amplitudes and speeds of rotation of the shaft, then nonlinear cubic damping can completely eliminate it. The varying amplitude (VAM) method is used to determine the nature of the system response, supplemented with the concept of “slow” time, which allows us to investigate and analyze the effect of nonlinear cubic damping and nonlinear rigidity of cubic order on the frequency response at a nonstationary resonant transition.

Most of the arm lifts used in today’s industry are designed and manufactured based on the scissor mechanism. Such schemes have one drawback: when the mechanism is raised, their connection points with the base and the movable platform narrow, which leads to a let-down in its stability. This article proposes a new scheme for the lifting device, which eliminates the above disadvantage of scissor schemes. In the scheme developed by the authors, the joints connecting the mechanism to the moving platform and the base are fixed, which means that the distance between the connection points does not change, leading to its stable operation. The mechanism consists of one group of links of the second class and two groups of links of the fourth class. The article focuses on the stability of an automotive lift’s design when moving with a load. The article presents the results of a kinematic and kinetostatic analysis, a study of the stability of the lift and the results of studies of an experimental sample of the developed lift. The methods presented in this article allow for the design of automotive lifts with new lever mechanisms, as demonstrated by computer modeling and experiments.

In dynamics of the orthogonal mechanism of vibrating table main attention is paid to the effect of friction on vibrational process when it is interacting with non-ideal energy source. As a result of analysis of numerical solutions of nonlinear equation of motion, it is established that in general, for the period of rotation, both sliding friction and rotational friction increase the difference between the maximum and minimum angular velocity values of the driving link (engine shaft) when its average value is constant; both increase the coefficient of non-uniformity of rotation. When there is a cargo of significant mass in the working link, the effect of sliding friction impacts more on the amplitude and frequency of the angular velocity oscillations of the driving link (engine shaft) and on the frequency of the coordinate changes, as well as on the frequencies and maximum and minimum values of the projections of the velocity and acceleration of the hinge linking the work platform to coupler. Similarly, the larger of the load mass, the stronger the effect of rotational friction on the amplitude and frequency of angular velocity oscillations of the driving link (engine shaft).

This article considers the oscillation of a solid body on kinematic foundations, the main elements of which are rolling bearers bounded by high-order surfaces of rotation at horizontal displacement of the foundation. Equations of motion of the vibro-protected body have been obtained. It is ascertained that the obtained equations of motion are highly nonlinear differential equations. Stationary and transitional modes of the oscillatory process of the system have been investigated. It is determined that several stationary regimes of the oscillatory process exist. Equations of motion have been investigated also by quantitative methods. In this paper the cumulative curves in the phase plane are plotted, a qualitative analysis for singular points and a study of them for stability are performed. In the Hayashi plane a cumulative curve of a body protected against vibration forms a closed path which does not tend to the stability of a singular point. This means that the vibration amplitude of a body protected against vibration does not remain constant in a steady state, but changes periodically.

Research on the dynamics of single-acting crank pump with damless hydro turbine drive