TO THE QUESTION OF ANALYSIS OF EQUATIONS OF MOTION OF A RIGID BODY DURING THE MECHANICAL OSCILATIONS

Depending on the current position of the mass in different areas of the spring deformation during the oscillation process the values that determines the natural frequency of free continuous oscillations have opposite signs. It is defined by the change in the direction of acceleration of the mass in these areas, which makes it possible to determine a single inhomogeneous differential equation of the oscillation process in different areas of the movement of the mass. When the oscillation amplitude is much less than the static position of the mass, this inhomogeneous differential equation represents a homogeneous differential equation of free undamped oscillations.

TO THE QUESTION OF ANALYSIS OF EQUATIONS OF MOTION OF A RIGID BODY DURING THE MECHANICAL OSCILATIONS

Depending on the current position of the mass in different areas of the spring deformation during the oscillation process the values that determines the natural frequency of free continuous oscillations have opposite signs. It is defined by the change in the direction of acceleration of the mass in these areas, which makes it possible to determine a single inhomogeneous differential equation of the oscillation process in different areas of the movement of the mass. When the oscillation amplitude is much less than the static position of the mass, this inhomogeneous differential equation represents a homogeneous differential equation of free undamped oscillations.

Analysis of Oscillations in Fractional Order LTI Systems

This paper is devoted to analysis of undamped oscillations generated by fractional order linear time invariant (LTI) systems. At first, the trajectories of marginally stable commensurate order systems are investigated. It is verified that we can not use the time-independent phase flow concept for this kind of systems. Also, the differences with the integer order case are highlighted. Then, it is shown that we can determine the Q-norm of the limit sets of a trajectory for these systems based on the Q-norm of the initial condition. Some numerical examples are brought to confirm the achievements of the paper.

Influence of Embankments With Parapets on the Cross-Wind Turbulence Intensity at the Contact Wire of Railway Overheads

Winds as an environmental factor can cause significant difficulties for the railway system operation. The railway overhead has been particularly vulnerable to cross-winds related problems, such as development of undamped oscillations due to galloping phenomenon. The installation of windbreaks to decrease the aerodynamic loads on the train can affect the loads on railway overheads triggering cable galloping. One essential parameter to indicate the influence of the parapet wake on the catenary contact wire is the turbulence intensity. In this paper the results of an experimental analysis of the turbulence intensity due to the presence of parapets carried out in a wind tunnel are reported. Embankments equipped with different parapets have been tested and turbulence intensity has been measured at both contact wire locations, windward and leeward. The relative influence of the parapets is measured through a reduced turbulence intensity, defined as the ratio between the turbulence intensity measured with parapet and the turbulence intensity in the case without any parapet on the embankment. In general the reduced turbulence intensity increases as the height of the parapet increases.