SYNCHRONOUS ELIMINATION OF VIBRATION IN THE PLANE, PART 1: ANALYSIS OF OCCURRENCE OF SYNCHRONOUS MOVEMENTS

A synchronous vibration eliminator applied to an object moving in a plane is investigated. The equation of motion of a system, which consists of a rigid object and several free rotating vibrators placed on this object, are introduced. Necessary conditions are found under which vibrators, moving synchronously with a force acting on an object, can eliminate object vibration. Computer simulation of an object and vibrators behaviour is done. Some time-runs of object vibrations and co-ordinates of vibrators positioning are shown. It was proven that in reality, elimination of vibration occurrence and vibrator movements stabilize in such a way that they move with constant velocities and phases. Simplified solutions of equation describing object movements were found, and then vibrator forces that induced vibrator movements were defined. It was found on which parameters these forces depend and how they change in relation to vibrator positions. The zero points of these forces were obtained and these points are the vibrators equilibrium positions. It was proven that by fulfilling certain conditions such positions of vibrators give full reduction of an objectʹs vibration.