Impact force generator: self-synchronization and regularity of motion

Abstract Impacts in multibody mechanical systems are an object of interest for many scientists in the world. In this paper, we present a principle of operation of the impact force generator being an element of the rotor of the heat exchanger. In this machine, step disturbances of the rotational velocity of the generator cause rapid changes of the rotational velocity of the exchanger rotor, which leads to the intensi®cation of the heat exchange process. We show the phenomenon of self-synchronization, regular motion of the system, and in a special case: chaotic motion of the rotor.

Synchronization of slowly rotating pendulums

We study synchronization of a number of rotating pendulums mounted on a horizontal beam which can roll on the parallel surface. It has been shown that after the initial transient different states of pendulums' synchronization occur. We derive the analytical equations for the estimation of the phase differences between phase synchronized pendulums. After study of the basins of attraction of different synchronization states we argue that the observed phenomena are robust as they occur in the wide range of both initial conditions and system parameters

Multi-headed chimera states in coupled pendula

We discuss the occurrence of the chimera states in the network of coupled, excited by the clock's mechanisms pendula. We find the patterns of multi-headed chimera states in which pendula clustered in different heads behave differently (oscillate with different frequencies) and create different types of synchronous states (complete or phase synchronization). The mathematical model of the network shows that the observed chimera states are controlled by elementary dynamical equations derived from the Newton's laws that are ubiquitous in many physical and engineering systems

Nonlinear dynamics and synchronisation of pendula attached to a rotating hub

A model of a nonlinear system composed of a hub with attached two pendula rotating in a horizontal plane is studied in the paper. Each single pendulum, treated as a stiff and massless rod with a lumped mass, is connected to the hub by a flapping hinge. Nonlinear stiffness and viscous damping of the hinge is taken into consideration. The system is excited by an external torque generated by a DC motor which is considered as an ideal system with torque given by a harmonic function. For small oscillations the problem is linearised and then solved analytically. An influence of the structural parameters like mass of the hub and pendula length on natural end excited vibrations is presented. Large oscillations are studied by a continuation technique, directly from the original Ordinary Differential Equations of motion (ODE). The complete synchronisation, phase synchronisation, bifurcations and transition through resonances are analysed considering the influence of the mass of the hub. The existence of chaotic oscillations of the system and paths leading to chaos are demonstrated as well