Study of synchronization for a rotor-pendulum system with Poincare method

A simplified model of the system of unbalanced rotors coupled with pendulum rod is examined. The model consists of two counter-rotating rotors, a rigid pendulum rod and a rigid vibrating body, which is horizontally connected to a fixed support by means of springs. The synchronous state of the system, i.e. synphase and antiphase synchronization of the rotors, is studied by means of the Poincare method. Moreover, the assessment of the synchronous state is converted to find a solution that should satisfy a balanced function and a stability function of the system. However, frequency ratios and installation angular are included in the two functions. It is demonstrated that the spring stiffness and the installation angular have a large influence on the existence and stability of the synchronization state in the coupling system. Finally, computer simulations are preformed to verify the theoretical computations

Theoretical study on self-synchronization of two homodromy rotors coupled with a pendulum rod in a far-resonant vibrating system

The objective of this paper is to investigate the self-synchronization of two homodromy rotors coupled with a pendulum rod in a far-resonant vibrating system. Using the average method and revisionary small parameters, we derive the dimensionless equation of the self-synchronization criterion and synchronous stability of the vibrating system. Meanwhile, to prove the correctness of the theoretical analysis, the diversity feature of the vibrating system is simulated numerically. Both results of theoretical analysis and numerical simulation show that increasing the length of the pendulum rod or decreasing the mass of the rotor connected with pendulum rod can ensure the self-synchronization and synchronous stability of two homodromy rotors in the vibrating system

Synchronization of the secondary isolation system with a dual-motor excitation

A dynamical model is proposed in this paper to study the synchronization and stability of the secondary isolation system with a dual-motor excitation. After deducing the dynamic equations of the system by Lagrange’s equation, the Laplace transform is used to deduce the displacement responses of the system when the system operate in steady state. The synchronous balance equation and stability condition of the system is derived with average method, and the relationship between the coefficient of synchronous ability and the geometric parameters of the system is discussed. It can be found that synchronization ability of the system is gradually increased with the increase between two motors mounting distance; meanwhile the larger difference of the mass between the two unbalanced rotors, the more difficult to implement synchronous operation of the system. Moreover, the stable phase difference of the vibrating system being as the key determinant to reach synchronization is discussed numerically. The research result shows that the synchronous behavior of the system is influenced by rotation direction of the rotors, mounting position of two motors, and mass ratios between unbalanced rotors and vibrating body. The correctness of theoretical analyses is verified by simulation results with Runge-Kutta method

Synchronization and Stability of Two Unbalanced Rotors with Fast Antirotation considering Energy Balance

We consider synchronization and stability of two unbalanced rotors reversely and fast excited by induction motors fixed on an oscillating body. We explore the energy balance of the system and show how the energy is transferred between the rotors via the oscillating body allowing the implementation of the synchronization of the two rotors. An approximate analytical analysis, energy balance method, allows deriving the synchronization condition, and the stability criterion of the synchronization is deduce by disturbance differential equations. Later, to prove the correctness of the theoretical analysis, many features of the vibrating system are computed and discussed by computer simulations. The proposed method may be useful for analyzing and understanding the mechanism of synchronization, stability, and energy balance of similar fast rotation rotors excited by induction motors in vibrating systems

rac-tert-Butyl 2-{5-[(4-{2-[methyl(pyri­din-2-yl)amino]ethoxy}phenyl)methyl]-2,4-dioxo-1,3-thiazolidin-3-yl}acetate

The title compound, C24H29N3O5S, is a chiral mol­ecule which crystallizes in a centrosymmetric space group as a racemate. The thia­zolidine ring forms the dihedral angles of 29.22 (12) and 67.79 (10)° with the benzene and pyridine rings, respectively. The benzene and pyridine rings are tilted by dihedral angle of 67.18 (9)°. In the crystal, inter­molecular C—H⋯O hydrogen bonds link the mol­ecules into a two-dimensional network

Joint Optimization of Active and Passive Beamforming in Multi-IRS Aided mmWave Communications

Intelligent reflecting surface (IRS) has been considered as a promising technology to alleviate the blockage effect and enhance coverage in millimeter wave (mmWave) communication. To explore the impact of IRS on the performance of mmWave communication, we investigate a multi-IRS assisted mmWave communication network and formulate a sum rate maximization problem by jointly optimizing the active and passive beamforming and the set of IRSs for assistance. The optimization problem is intractable due to the lack of convexity of the objective function and the binary nature of the IRS selection variables. To tackle the complex non-convex problem, an alternating iterative approach is proposed. In particular, utilizing the fractional programming method to optimize the active and passive beamforming and the optimization of IRS selection is solved by enumerating. Simulation results demonstrate the performance gain of our proposed approach.Comment: 6 pages, 4 figures, accepted by IEEE GLOBECOM 202