Investigation of oscillations of platform on isotropic supports excited by a pendulum

Central Ukrainian National Technical University, 25006, Kropyvnytskyi, Universytetskyi Ave., 8, Ukraine

^* Corresponding author: filimonikhin@ukr.net

Abstract

Within the framework of a flat model, steady-state modes of motion of a system composed of a platform on isotropic elastic-viscous supports, a shaft on a platform, and a pendulum freely mounted on a shaft are investigated. The developed methodology was used in the studies, based on the energy method, the theory of bifurcations of motions, and the idea of a parametric solution to the problem. All steady-state modes of motion were found. It is established that these are modes of the pendulum jamming. Each mode is characterized by a corresponding jamming frequency. Depending on the velocity of rotation of the shaft, there may be one or three possible jamming frequencies. When there is only one jamming frequency, the corresponding mode of motion is globally asymptotically stable. When there are three jamming frequencies, locally asymptotically stable modes with the smallest and highest jamming frequencies of the pendulum. The smallest jamming frequency of the pendulum is close to resonance. This mode can be used to excite resonant vibrations in vibrating machines. The highest jamming frequency of a pendulum is close to the shaft rotation velocity. This mode can be used to excite non-resonant vibrations in vibrating machines.