CALCULATION OF A TRAJECTORY FOR THE MOVEMENT OF A LOAD OF SWINGING SPRING

Abstract

Pendulum oscillations in the vertical plane of a suspended weightless spring, while maintaining the straightness of its axis, are considered. In the literature, this type of pendulum is called a swinging spring. The required trajectory of the load of the swinging spring is modeled using a computer using the values ​​of the mass of the load, the stiffness of the spring and its length without load. In addition, the initial values ​​of the parameters for initiating oscillations of the oscillating spring are used: the initial angle of deviation of the spring axis from the vertical, the initial rate of change of this angle, as well as the initial parameter of the spring elongation and the initial rate of change of the elongation. The calculations were performed using the Lagrange equation of the second kind. Variants of finding conditionally periodic trajectories of movement of a point load of a swinging spring with a movable attachment point are considered.
 The relevance of the topic is determined by the need to research and improve new technological schemes of mechanical devices, which include springs. In particular, the study of the conditions for separating from chaotic vibrations of mechanical structure elements and determining the rational values ​​of parameters to ensure periodic trajectories of their vibrations.
 Calculation options are given to obtain periodic trajectories of cargo movement, when the given parameters are:
 - the length of the spring without load and its stiffness with an unknown value of the mass of the load;
 - the length of the spring without load and the value of the mass of the load with an unknown spring stiffness;
 - the value of the mass of the load and the stiffness of the spring with an unknown length of the spring without load.
 The results can be used as a paradigm for studying nonlinear coupled systems, as well as for calculating options for mechanical devices, when it is necessary to dissociate themselves from chaotic movements of loads, and provide periodic trajectories of their movement.